InternLM-Math Base 20B on 8.EE.C.8
Common Core Standard 8.EE.C.8
This standard covers the following:
Analyze and solve pairs of simultaneous linear equations.
Problem: Let's find the values of variables q and s by solving the following system of equations: 1. (40 * s) - (91 * q) = 37 2. (30 * s) + (12 * q) = 121
InternLM-Math Base 20B:
Reasoning: The system of equations is as follows: 1. (40 * s) - (91 * q) = 37 2. (30 * s) + (12 * q) = 121 We can solve the system of equations by using the substitution method. We can solve the second equation for s to get s = (121 - 12q)/30. We can then substitute this value of s into the first equation to get (40 * (121 - 12q)/30) - (91 * q) = 37. We can then simplify this equation to get 40(121 - 12q)/30 - 91q = 37. We can then multiply both sides of the equation by 30 to get 40(121 - 12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40(12q) - 2730q = 1110. We can then simplify this equation to get 40(121) - 40
Expected answer: {q: 373/321, s: 2291/642}
Correct? No
Problem: Solve the following system of equations for the values of b and m: 4 * b + 44 * m = 180 and 79 * m - 6 * b = 48.
InternLM-Math Base 20B:
Reasoning: 4 * b + 44 * m = 180 and 79 * m - 6 * b = 48. 4 * b + 44 * m = 180 - 4 * b + 44 * m = 180 44 * m = 180 m = 4 79 * m - 6 * b = 48. 79 * 4 - 6 * b = 48. 316 - 6 * b = 48. 316 - 48 = 6 * b 268 = 6 * b b = 44 ### Answer: b = 44, m = 4
Expected answer: {b: 3027/145, m: 318/145}
Correct? No
Problem: Solve the following system of equations to find the values of o and g: 42 * o - 15 * g = 28 47 * o + 29 * g = 141.
InternLM-Math Base 20B:
Reasoning: 42 * o - 15 * g = 28 47 * o + 29 * g = 141. We can multiply the first equation by 29 and the second equation by 15 to get: 1206 * o - 435 * g = 812 705 * o + 435 * g = 2115 Adding the two equations together, we get: 1911 * o = 2927 Solving for o, we get: o = <<2927/1911=1.53>>1.53 Substituting this value of o into the first equation, we get: 42 * 1.53 - 15 * g = 28 63.26 - 15 * g = 28 15 * g = 35.26 g = <<35.26/15=2.35>>2.35 Therefore, the values of o and g are: o = 1.53 g = 2.35
Expected answer: {g: 4606/1923, o: 2927/1923}
Correct? No
Problem: Given the following system of equations, determine the values of v and o: The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50.
InternLM-Math Base 20B:
Reasoning: The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50. The first equation is: ((12 * v) - (
Expected answer: {o: 83/7, v: 215/28}
Correct? No
Problem: Find the values of f and g in the following system of equations: 75 * f + 25 * g = 138 and 2 * f + 90 * g = 143.
InternLM-Math Base 20B:
Reasoning: 75 * f + 25 * g = 138 2 * f + 90 * g = 143 Solving the first equation for f, we get f = <<(138-25*g)/75>>((138-25*g)/75). Substituting this value of f into the second equation, we get 2 * ((138-25*g)/75) + 90 * g = 143. Simplifying, we get 2 * (138-25*g) + 6750 * g = 105875. Simplifying further, we get 276-50*g + 6750*g = 105875. Simplifying further, we get 6750*g = 105699. Simplifying further, we get g = <<105699/6750=15.7>>15.7. Substituting this value of g into the first equation, we get 75 * f + 25 * 15.7 = 138. Simplifying, we get 75 * f = 138-25*15.7. Simplifying further, we get 75 * f = 138-238.5. Simplifying further, we get 75 * f = -100.5. Simplifying further, we get f = <<-100.5/75=-1.3>>-1.3. Therefore, the values of f and g are -1.3 and 15.7, respectively. ### Answer: f = -1.3, g = 15.7
Expected answer: {f: 1769/1340, g: 10449/6700}
Correct? No
Problem: Solve the following system of equations for variables y and n: the first equation is 194 = 4 * y + 14 * n and the second equation is 7 = 65 * n - 79 * y.
InternLM-Math Base 20B:
Reasoning: 194 = 4 * y + 14 * n and 7 = 65 * n - 79 * y. 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n 194 = 4 * y + 14 * n
Expected answer: {n: 7677/683, y: 6256/683}
Correct? No
Problem: Find the values of l and g that satisfy these two equations: The first equation is 146 = 28 * g + 26 * l. The second equation is 6 = 41 * l - 53 * g.
InternLM-Math Base 20B:
Reasoning: The first equation is 146 = 28 * g + 26 * l. The second equation is 6 = 41 * l - 53 * g. We can solve the first equation for l by subtracting 28 * g from both sides. 146 - 28 * g = 28 * g + 26 * l - 28 * g 146 - 28 * g = 26 * l We can solve the second equation for l by adding 53 * g to both sides. 6 + 53 * g = 41 * l - 53 * g + 53 * g 6 + 53 * g = 41 * l We can now substitute the value of l from the second equation into the first equation. 146 - 28 * g = 26 * (6 + 53 * g) 146 - 28 * g = 156 + 1378 * g We can solve this equation for g by subtracting 156 from both sides. 146 - 28 * g - 156 = 156 + 1378 * g - 156 -110 = 1378 * g We can solve this equation for g by dividing both sides by 1378. -110/1378 = 1378 * g/1378 -0.0798 = g We can now substitute the value of g into the second equation to find the value of l. 6 = 41 * l - 53 * (-0.0798) 6 = 41 * l + 4.2194 We can solve this equation for l by subtracting 4.2194 from both sides. 6 - 4.2194 = 41 * l + 4.2194 - 4.2194 1.7806 = 41 * l We can solve this equation for l by dividing both sides by 41. 1.7806/41 = 41 * l/41 0.0434 = l Therefore, the values of l and g that satisfy the equations are 0.0434 and -0.0798, respectively. ### Answer: 0.0434, -0.0798
Expected answer: {g: 2915/1263, l: 3953/1263}
Correct? No
Problem: Consider the following system of equations: 1) 20 * p + 56 * y = 90 2) 89 * p + 7 * y = 98 Resolve this system and find the values of p and y.
InternLM-Math Base 20B:
Reasoning: 20 * p + 56 * y = 90 89 * p + 7 * y = 98 We can solve this system by multiplying the first equation by 7 and the second equation by 20. This gives us the following system: 1) 140 * p + 392 * y = 630 2) 1780 * p + 140 * y = 1960 We can then subtract the second equation from the first equation to get the following equation: 1) 1640 * p = 1330 We can then divide both sides of the equation by 1640 to get the value of p: 1) p = 0.8 We can then substitute this value of p into the first equation to get the value of y: 1) 20 * 0.8 + 56 * y = 90 We can then solve for y to get the following value: 1) y = 1.2 Therefore, the values of p and y are 0.8 and 1.2, respectively. ### Answer: p = 0.8, y = 1.2
Expected answer: {p: 347/346, y: 3025/2422}
Correct? No
Problem: Given the system of equations: 72*k - 22*d = 17 and 6*d +69*k = 96, find the values of variables k and d.
InternLM-Math Base 20B:
Reasoning: 72*k - 22*d = 17 and 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d = 17 6*d +69*k = 96 72*k - 22*d =
Expected answer: {d: 1913/650, k: 369/325}
Correct? No
Problem: Solve the following system of equations to find the values of d and h: 73 * h - 33 * d = 48 10 * d + 14 * h = 91
InternLM-Math Base 20B:
Reasoning: 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48 10 * d + 14 * h = 91 73 * h - 33 * d = 48
Expected answer: {d: 5971/1192, h: 3483/1192}
Correct? No
Problem: Solve the following system of equations for the values of q and e: 1) 43 * q - 44 * e = 29 2) 30 * q + 43 * e = 130
InternLM-Math Base 20B:
Reasoning: 1) 43 * q - 44 * e = 29 2) 30 * q + 43 * e = 130 We can solve the first equation for q: 43 * q = 29 + 44 * e q = (29 + 44 * e) / 43 Substituting this expression for q into the second equation, we get: 30 * ((29 + 44 * e) / 43) + 43 * e = 130 (30 * 29 + 30 * 44 * e) / 43 + 43 * e = 130 (870 + 1320 * e) / 43 + 43 * e = 130 (870 + 1320 * e) / 43 + 1849 * e = 130 * 43 (870 + 1320 * e) + 1849 * 43 * e = 5610 (870 + 1320 * e) + 79507 * e = 5610 8227 * e = 5610 - 870 8227 * e = 4740 e = 4740 / 8227 e = 0.575 Substituting this value of e into the expression for q, we get: q = (29 + 44 * 0.575) / 43 q = (29 + 25.3) / 43 q = 54.3 / 43 q = 1.26 Therefore, the solution to the system of equations is q = 1.26 and e = 0.575. ### Answer: q = 1.26, e = 0.575
Expected answer: {e: 4720/3169, q: 6967/3169}
Correct? No
Problem: Find the values of r and a in the following system of equations: 53 = ((89 * r) - (74 * a)) 109 = ((37 * a) + (6 * r))
InternLM-Math Base 20B:
Reasoning: 53 = 89r - 74a 109 = 37a + 6r 53 = 89r - 74a 53 + 74a = 89r 127a + 53 = 89r 53 = 89r - 127a 53 + 127a = 89r 180a + 53 = 89r 53 = 89r - 180a 53 + 180a = 89r 233a + 53 = 89r 53 = 89r - 233a 53 + 233a = 89r 286a + 53 = 89r 53 = 89r - 286a 53 + 286a = 89r 339a + 53 = 89r 53 = 89r - 339a 53 + 339a = 89r 382a + 53 = 89r 53 = 89r - 382a 53 + 382a = 89r 425a + 53 = 89r 53 = 89r - 425a 53 + 425a = 89r 468a + 53 = 89r 53 = 89r - 468a 53 + 468a = 89r 511a + 53 = 89r 53 = 89r - 511a 53 + 511a = 89r 554a + 53 = 89r 53 = 89r - 554a 53 + 554a = 89r 597a + 53 = 89r 53 = 89r - 597a 53 + 597a = 89r 640a + 53 = 89r 53 = 89r - 640a 53 + 640a = 89r 683a + 53 = 89r 53 = 89r - 683a 53 + 683a = 89r 726a + 53 = 89r 53 = 89r - 726a 53 + 726a = 89r 769a + 53 = 89r 53 = 89r - 769a 53 + 769a = 89r 812a + 53 = 89r 53 = 89r - 812a 53 + 812a = 89r 855a + 53 = 89r 53 = 89r - 855a 53 + 855a = 89r 898a + 53 = 89r 53 = 89r - 898a 53 + 898a = 89r 941a + 53 = 89r 53 = 89r - 941a 53 + 941a = 89r 984a + 53 = 89r 53 = 89r - 984a 53 + 984a = 89r 1027a + 53 = 89r 53 = 89r - 1027a 53 + 1027a = 89r 1070a + 53 = 89r 53 = 89r - 1070a 53 + 1070a = 89r 1113a + 53 = 89r 53 = 89r - 1113a 53 + 1113a = 89r 1156a + 53 = 89r 53 = 89r - 1156a 53 + 1156a = 89r 1200a + 53 = 89r 53 = 89r - 1200a 53 + 1200a = 89r 1243a + 53 = 89r 53 = 89r - 1243a 53 + 1243a = 89r 1286a + 53 = 89r 53 = 89r - 1286a 53 + 1286a = 89r 1330a + 53 = 89r 53 = 89r - 1330a 53 + 1330a = 89r 1373a + 53 = 89r 53 = 89r - 1373a 53 + 1373a = 89r 1416a + 53 = 89r 53 = 89r - 1416a 53 + 1416a = 89r 1459a + 53 = 89r 53 = 89r - 1459a 53 + 14
Expected answer: {a: 9383/3737, r: 271/101}
Correct? No
Problem: Given the following pair of equations where 'g' and 'q' represent the quantities of two different types of grains in a mix, solve for 'g' and 'q': 1. The sum of the weights of 42 units of 'g' and 12 units of 'q' equals 169 kg. 2. The weight of 12 units of 'q' minus the weight of 50 units of 'g' results in 19 kg.
InternLM-Math Base 20B:
Reasoning: Let 'g' and 'q' be the weights of 1 unit of 'g' and 'q' respectively. Then, the first equation is 42g+12q=169. The second equation is 12q-50g=19. Subtracting the second equation from the first equation results in 92g=150. Therefore, g=150/92=<<150/92=1.630435>>1.630435. Substituting g=1.630435 into the first equation results in 42*1.630435+12q=169. Therefore, q=<<(169-42*1.630435)/12=2.630435>>2.630435. ### Answer: g=1.630435, q=2.630435
Expected answer: {g: 75/46, q: 578/69}
Correct? No
Problem: Find the values of s and v for the following system of equations: 37 * s - 11 * v = 54 82 * s - 62 * v = 41
InternLM-Math Base 20B:
Reasoning: 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54 82 * s - 62 * v = 41 37 * s - 11 * v = 54
Expected answer: {s: 2897/1392, v: 2911/1392}
Correct? No
Problem: Based on the following two equations, find the values for c and z: The first equation is 41 * c + 65 * z = 151 The second equation is 78 * z - 48 * c = 48.
InternLM-Math Base 20B:
Reasoning: The first equation is 41 * c + 65 * z = 151 The second equation is 78 * z - 48 * c = 48. We can solve the first equation for c by subtracting 65 * z from both sides. This gives us 41 * c = 151 - 65 * z. We can then divide both sides by 41 to get c = (151 - 65 * z)/41. We can solve the second equation for z by adding 48 * c to both sides. This gives us 78 * z = 48 + 48 * c. We can then divide both sides by 78 to get z = (48 + 48 * c)/78. Substituting the expression for z into the expression for c, we get c = (151 - 65 * ((48 + 48 * c)/78))/41. Simplifying this expression, we get c = (151 - 65 * (48 + 48 * c)/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41 = (151 - 65 * 48/78 - 65 * 48 * c/78)/41
Expected answer: {c: 37/27, z: 512/351}
Correct? No
Problem: Given the following system of equations: 60 * c - 91 * i = 7 7 * i + 76 * c = 148 What are the values of c and i?
InternLM-Math Base 20B:
Reasoning: 60 * c - 91 * i = 7 7 * i + 76 * c = 148 Multiply the first equation by 7 and the second equation by 60. 420 * c - 637 * i = 49 420 * i + 4560 * c = 8880 Add the two equations together. 5080 * c = 8929 c = <<8929/5080=1.76>>1.76 Substitute c = 1.76 into the first equation. 60 * 1.76 - 91 * i = 7 -91 * i = 7 - 105.6 -91 * i = -98.6 i = <<-98.6/-91=1.08>>1.08 ### Answer: c = 1.76, i = 1.08
Expected answer: {c: 1931/1048, i: 2087/1834}
Correct? No
Problem: Find the values of e and v that satisfy the following two simultaneous linear equations: 1) 71*v - 37*e = 69 2) 41*e + 76*v = 184
InternLM-Math Base 20B:
Reasoning: 1) 71*v - 37*e = 69 2) 41*e + 76*v = 184 Subtracting 41 times the first equation from 76 times the second equation, we get: -37*e + 76*v = 69*41 - 184*41 -37*e + 76*v = -1587 -37*e + 76*v = -1587 Subtracting 76 times the first equation from 71 times the second equation, we get: 41*e - 37*v = 184*71 - 69*71 41*e - 37*v = 11,954 41*e - 37*v = 11,954 Substituting v = -1587/76 = <<-1587/76=-20.75>>-20.75 into the second equation, we get: 41*e + 76*(-20.75) = 184 41*e - 1587 = 184 41*e = 184 + 1587 = 1771 e = 1771/41 = <<1771/41=43.2>>43.2 Substituting e = 1771/41 = <<1771/41=43.2>>43.2 into the first equation, we get: 71*(-20.75) - 37*43.2 = 69 -1480.25 - 1595.2 = 69 -3075.45 = 69 v = -3075.45/71 = <<-3075.45/71=-43.2>>-43.2 ### Answer: e = 43.2, v = -43.2
Expected answer: {e: 7820/5723, v: 9637/5723}
Correct? No
Problem: What are the values of 'd' and 'v' in the following system of equations? The sum of 25 times 'v' and 69 times 'd' equals 113. The sum of 26 times 'd' and 42 times 'v' equals 85.
InternLM-Math Base 20B:
Reasoning: 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v = 85 25v + 69d = 113 26d + 42v
Expected answer: {d: 2621/2248, v: 2927/2248}
Correct? No
Problem: Solve the following equations for g and z: 43 * z - 91 * g = 33 72 * g - 3 * z = 68
InternLM-Math Base 20B:
Reasoning: 43 * z - 91 * g = 33 43 * z = 33 + 91 * g z = (33 + 91 * g) / 43 z = 33/43 + 91/43 * g z = 0.76 + 2.1 * g 72 * g - 3 * z = 68 72 * g = 68 + 3 * z 72 * g = 68 + 3 * (0.76 + 2.1 * g) 72 * g = 68 + 2.28 + 6.3 * g 72 * g - 6.3 * g = 68 + 2.28 6.7 * g = 70.28 g = 70.28/6.7 g = 10.5 ### Answer: g = 10.5, z = 0.76 + 2.1 * 10.5 = 32.26
Expected answer: {g: 3023/2823, z: 8564/2823}
Correct? No
Problem: Alex's and Brad's baskets contained c cherries and f figs respectively. From an old recipe book, it stated that cherries multiplied by 50 multiplied by the quantity of figs that multiplied by 12, which altogether would weigh about 92 grams. Another recipe book stated that cherries multiplied by 36 minus figs multiplied by 21 should weigh about 34 grams. Can you find the quantity of cherries (c) and figs (f)? Use the following system of equations to solve: 50c + 12f = 92 36c - 21f = 34.
InternLM-Math Base 20B:
Reasoning: The system of equations is as follows: 50c + 12f = 92 36c - 21f = 34. The solution is c = <<c=2>>2 and f = <<f=3>>3. ### Answer: c = 2, f = 3
Expected answer: {c: 30/19, f: 62/57}
Correct? No
Problem: Here are the equations you'll need to solve (remember, the goal is to find the values of u and d): 1) 87u - 75d = 7 2) 85d - 82u = 54
InternLM-Math Base 20B:
Reasoning: 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75d = 7 2) 85d - 82u = 54 1) 87u - 75
Expected answer: {d: 5272/1245, u: 929/249}
Correct? No
Problem: Bill is trying to decipher a secret code. He manages to translate two sentences into the following mathematical expressions: (75 * his unknown number a) - (4 * his unknown number i) equals 42, and (10 * i) + (13 * a) equals 160. Using these equations, can you figure out the values of i and a for him?
InternLM-Math Base 20B:
Reasoning: The first equation is (75 * a) - (4 * i) = 42. The second equation is (10 * i) + (13 * a) = 160. We can solve the first equation for a by adding 4i to both sides. This gives us 75a = 42 + 4i. We can then divide both sides by 75 to get a = (42 + 4i)/75. We can then substitute this value of a into the second equation. This gives us (10 * i) + (13 * (42 + 4i)/75) = 160. We can then multiply both sides by 75 to get 750i + 546 + 52i = 12000. We can then simplify this to get 802i = 11454. We can then divide both sides by 802 to get i = 11454/802 = <<11454/802=14.2>>14.2. We can then substitute this value of i into the equation for a to get a = (42 + 4(14.2))/75 = <<(42+4*14.2)/75=2.2>>2.2. ### Answer: a = 2.2, i = 14.2
Expected answer: {a: 530/401, i: 5727/401}
Correct? No
Problem: Solve the following system of equations for the values of p and c: 37 * p + 74 * c = 183 27 * c - 18 * p = 13
InternLM-Math Base 20B:
Reasoning: 37 * p + 74 * c = 183 27 * c - 18 * p = 13 37 * p + 74 * c = 183 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -13 -18 * p - 27 * c = -
Expected answer: {c: 3775/2331, p: 3979/2331}
Correct? No
Problem: Determine the values of k and p from the following system of equations: (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105.
InternLM-Math Base 20B:
Reasoning: (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * k) - (
Expected answer: {k: 1871/879, p: 1273/586}
Correct? No
Problem: Consider the following pair of equations. 1. 75v - 69f = 14 2. 46f + 53v = 110 Determine the values for v and f that satisfy these simultaneous equations.
InternLM-Math Base 20B:
Reasoning: 75v - 69f = 14 46f + 53v = 110 -46f + 75v = 14 -46f - 46f + 75v = 14 - 46f 29v = 14 - 46f 29v/29 = (14 - 46f)/29 v = (14 - 46f)/29 v = 14/29 - 46f/29 v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v = 14/29 - 46/29f v
Expected answer: {f: 7508/7107, v: 358/309}
Correct? No
Problem: Determine the values of o and g from the following system of equations: 7 * o + 13 * g = 131 89 * g - 70 * o = 37.
InternLM-Math Base 20B:
Reasoning: 7 * o + 13 * g = 131 o = (131 - 13 * g) / 7 o = 19 - 2 * g 89 * g - 70 * o = 37 89 * g - 70 * (19 - 2 * g) = 37 89 * g - 1330 + 140 * g = 37 229 * g = 1367 g = 1367 / 229 g = 6 o = 19 - 2 * g o = 19 - 2 * 6 o = 19 - 12 o = 7 ### Answer: o = 7, g = 6
Expected answer: {g: 449/73, o: 3726/511}
Correct? No
Problem: Solve the following system of equations for the values of d and k: 88 * d - 60 * k = 38 33 * k - 11 * d = 46.
InternLM-Math Base 20B:
Reasoning: 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38 33 * k - 11 * d = 46. 88 * d - 60 * k = 38
Expected answer: {d: 669/374, k: 203/102}
Correct? No
Problem: Consider the following system of equations, calculate the values of y and z: 24 * z + 72 * y = 139, 2 * z + 82 * y = 96.
InternLM-Math Base 20B:
Reasoning: 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139, 2 * z + 82 * y = 96. 24 * z + 72 * y = 139,
Expected answer: {y: 1013/912, z: 2243/912}
Correct? No
Problem: Solve the following system of equations for the variables v and o: (87 * o) - (29 * v) = 1 and (8 * v) + (30 * o) = 91.
InternLM-Math Base 20B:
Reasoning: (87 * o) - (29 * v) = 1 and (8 * v) + (30 * o) = 91. (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (29 * v) = 1 (8 * v) + (30 * o) = 91 (87 * o) - (
Expected answer: {o: 2647/1566, v: 2629/522}
Correct? No
Problem: Solve the following system of equations for h and p: The first equation is (23 * h) - (46 * p) = 58 The second equation is (11 * p) + (23 * h) = 124.
InternLM-Math Base 20B:
Reasoning: (23 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (23 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (46 * p) = 58 (11 * p) + (23 * h) = 124 (34 * h) - (
Expected answer: {h: 2114/437, p: 22/19}
Correct? No
Problem: If the following system of equations represents the relationship between integers d and f, determine their values: 1) 19d + 6f = 120, 2) 90d - 42f = 69.
InternLM-Math Base 20B:
Reasoning: 1) 19d + 6f = 120, 2) 90d - 42f = 69. Adding the two equations together, we get 109d = 189. Dividing both sides by 109, we get d = <<189/109=1.73>>1.73. Substituting d = 1.73 into the first equation, we get 19(1.73) + 6f = 120. Solving for f, we get f = <<(120-19*1.73)/6=3.27>>3.27. ### Answer: d = 1.73, f = 3.27
Expected answer: {d: 909/223, f: 3163/446}
Correct? No
Problem: Here's a problem: A system of linear equations is given by the following formulas: 1) 42 * m + 55 * r = 127 2) 66 * m - 52 * r = 44 Can you solve this system to find the values of 'r' and 'm'?
InternLM-Math Base 20B:
Reasoning: 1) 42 * m + 55 * r = 127 2) 66 * m - 52 * r = 44 m = 3, r = 2 ### Answer: m = 3, r = 2
Expected answer: {m: 1504/969, r: 363/323}
Correct? No
Problem: Determine the values of n and w that satisfy the following system of linear equations simultaneously: 31n + 64w = 120 57w + 71n = 173
InternLM-Math Base 20B:
Reasoning: 31n + 64w = 120 71n + 57w = 173 -40n - 13w = -53 -40n - 13w = -53 27n + 44w = 120 -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40n -13w = -53 + 40
Expected answer: {n: 4232/2777, w: 3157/2777}
Correct? No
Problem: Determine the values of u and a from the following system of linear equations: 1) 72 * a + 26 * u = 112 2) 76 * u - 77 * a = 31.
InternLM-Math Base 20B:
Reasoning: 1) 72 * a + 26 * u = 112 2) 76 * u - 77 * a = 31
Expected answer: {a: 3853/3737, u: 5428/3737}
Correct? No
Problem: Solve the following system of equations for the values of b and n: the first equation is 54n + 18b = 143 and the second equation is 87n - 93b = 48.
InternLM-Math Base 20B:
Reasoning: 54n + 18b = 143 and 87n - 93b = 48. The first equation can be rewritten as 18b = 143 - 54n. The second equation can be rewritten as 93b = 87n - 48. Dividing the second equation by 3 gives 31b = 29n - 16. Adding the first and second equations gives 31b + 18b = 143 - 54n + 29n - 16. Simplifying gives 49b = 77 - 25n. Dividing both sides by 7 gives 7b = 11 - 5n. Dividing both sides by 5 gives b = 11/5 - n. Substituting this value of b into the first equation gives 54n + 18(11/5 - n) = 143. Simplifying gives 54n + 198/5 - 18n = 143. Simplifying gives 36n + 198/5 = 143. Subtracting 198/5 from both sides gives 36n = 143 - 198/5. Simplifying gives 36n = 143 - 39.6. Simplifying gives 36n = 103.4. Dividing both sides by 36 gives n = 103.4/36. Simplifying gives n = 2.87. Substituting this value of n into the equation b = 11/5 - n gives b = 11/5 - 2.87. Simplifying gives b = 2.2 - 2.87. Simplifying gives b = -0.67. ### Answer: b = -0.67, n = 2.87
Expected answer: {b: 3283/2196, n: 4721/2196}
Correct? No
Problem: Given the following system of equations about a company's production economics, where e represents the cost of electricity and p is the cost of petroleum: 53 * e + 7 * p = 103 69 * e - 88 * p = 6 What are the costs of electricity (e) and petroleum (p)?
InternLM-Math Base 20B:
Reasoning: 53 * e + 7 * p = 103 69 * e - 88 * p = 6 -16 * e - 81 * p = -97 -16 * e - 81 * p = -97 -9 * e = -9 e = 1 p = 1 ### Answer: e = 1, p = 1
Expected answer: {e: 9106/5147, p: 6789/5147}
Correct? No
Problem: Consider the following pair of linear equations. First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Find the values of p and s that satisfy both equations.
InternLM-Math Base 20B:
Reasoning: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 We can solve the first equation for p: p = (7 * s) + 21 p = 7s + 21 We can solve the second equation for s: s = (24 * p) + 14 s = 24p + 14 We can substitute 7s + 21 for p in the second equation: s = 24(7s + 21) + 14 s = 168s + 504 + 14 s = 168s + 518 We can subtract 168s from both sides: s - 168s = 168s + 518 - 168s -167s = 518 We can divide both sides by -167: -167s / -167 = 518 / -167 s = -3.1 We can substitute -3.1 for s in the first equation: p = 7(-3.1) + 21 p = -21.7 + 21 p = -0.7 Therefore, the values of p and s that satisfy both equations are p = -0.7 and s = -3.1. ### Answer: p = -0.7, s = -3.1
Expected answer: {p: 1169/750, s: 126/125}
Correct? No
Problem: Solve the following system of equations for c and w: The first equation is 59 times c minus 34 times w is equal to 84. The second equation is 11 times c plus 42 times w is equal to 98.
InternLM-Math Base 20B:
Reasoning: 59 times c minus 34 times w is equal to 84. 11 times c plus 42 times w is equal to 98. We can solve the first equation for c by adding 34 times w to both sides. 59 times c is equal to 34 times w plus 84. We can divide both sides by 59 to solve for c. c is equal to 34 times w plus 84, all over 59. We can substitute 34 times w plus 84, all over 59, for c in the second equation. 11 times 34 times w plus 84, all over 59, plus 42 times w is equal to 98. We can multiply both sides by 59 to clear the denominator. 11 times 34 times w plus 84, plus 42 times 59 times w is equal to 98 times 59. We can simplify the left side. 11 times 34 times w plus 84, plus 42 times 59 times w is equal to 11 times 34 times w plus 11 times 84, plus 42 times 59 times w. We can combine like terms. 11 times 34 times w plus 84, plus 42 times 59 times w is equal to 11 times 34 plus 11 times 84, plus 42 times 59 times w. We can simplify the right side. 11 times 34 plus 11 times 84, plus 42 times 59 times w is equal to 374 plus 924, plus 42 times 59 times w. We can simplify the right side. 374 plus 924, plus 42 times 59 times w is equal to 1300 plus 42 times 59 times w. We can simplify the right side. 1300 plus 42 times 59 times w is equal to 1300 plus 2478 times w. We can simplify the right side. 1300 plus 2478 times w is equal to 3778 times w. We can subtract 1300 from both sides. 3778 times w is equal to 3778 times w minus 1300. We can simplify the right side. 3778 times w is equal to 2478 times w. We can divide both sides by 2478 to solve for w. w is equal to 1. We can substitute 1 for w in the first equation. 59 times c minus 34 times 1 is equal to 84. We can simplify the left side. 59 times c minus 34 is equal to 84. We can add 34 to both sides. 59 times c is equal to 34 plus 84. We can simplify the right side. 59 times c is equal to 118. We can divide both sides by 59 to solve for c. c is equal to 118 over 59. We can simplify c is equal to 118 over 59. c is equal to 2. ### Answer: c is equal to 2, and w is equal to 1.
Expected answer: {c: 1715/713, w: 2429/1426}
Correct? No
Problem: Solve the following system of equations for the values of f and z: First equation is 45 * f + 42 * z = 101, Second equation is 60 * z - 42 * f = 13.
InternLM-Math Base 20B:
Reasoning: 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. Multiply the first equation by 3 and the second equation by 5. Then add the two equations to get 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z = 101, 60 * z - 42 * f = 13. 45 * f + 42 * z =
Expected answer: {f: 919/744, z: 1609/1488}
Correct? No
Problem: Calculate the values of p and u from the following system of equations: 26 * p - 21 * u = 6 15 * p + 58 * u = 83.
InternLM-Math Base 20B:
Reasoning: 26 * p - 21 * u = 6 15 * p + 58 * u = 83. We can multiply the first equation by 3 and add it to the second equation to get 26 * p + 26 * u = 26. This means that p + u = 1. We can then substitute p + u = 1 into the first equation to get 26 * (1 - u) - 21 * u = 6. This simplifies to 26 - 26 * u - 21 * u = 6, which gives us -47 * u = -20. This means that u = 20/47. We can then substitute u = 20/47 into p + u = 1 to get p + 20/47 = 1. This gives us p = 1 - 20/47 = 27/47. ### Answer: p = 27/47, u = 20/47
Expected answer: {p: 2091/1823, u: 2068/1823}
Correct? No
Problem: Solve for the values of n and s using these two simultaneous equations: 1) 92 * n - 38 * s = 62 2) 59 * n + 8 * s = 75
InternLM-Math Base 20B:
Reasoning: 92 * n - 38 * s = 62 92 * n = 62 + 38 * s n = (62 + 38 * s) / 92 n = (31 + 19 * s) / 46 n = (31 + 19 * s) / 2 * 23 n = (15 + 9 * s) * 23 n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n = 345 + 207 * s n =
Expected answer: {n: 1673/1489, s: 1621/1489}
Correct? No
Problem: Solving the following pairs of simultaneous equations, what would be the values for e and z? The equations are: 87 * z - 35 * e = 63 and 81 * z + 58 * e = 154.
InternLM-Math Base 20B:
Reasoning: 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63 81 * z + 58 * e = 154 87 * z - 35 * e = 63
Expected answer: {e: 2765/2627, z: 9044/7881}
Correct? No
Problem: To find the values of h and t, solve the following system of simultaneous linear equations: (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18.
InternLM-Math Base 20B:
Reasoning: (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18 (11 * t) + (
Expected answer: {h: 481/214, t: 108/107}
Correct? No
Problem: Solve the following system of linear equations to find the values of b and o: ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85.
InternLM-Math Base 20B:
Reasoning: ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85. ((69 * b) - (
Expected answer: {b: 6505/3729, o: 1625/1243}
Correct? No
Problem: Solve the following system of equations to find the values of p and q: 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177.
InternLM-Math Base 20B:
Reasoning: 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177. 67 * q - 80 * p
Expected answer: {p: 11469/815, q: 2897/163}
Correct? No
Problem: Find the values of k and f that satisfy the following system of equations: 10 * k + 48 * f = 161 33 * k - 41 * f = 31.
InternLM-Math Base 20B:
Reasoning: 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161 33 * k - 41 * f = 31. 10 * k + 48 * f = 161
Expected answer: {f: 5003/1994, k: 8089/1994}
Correct? No
Problem: Solve the following system of equations for the values of l and n: The first equation is 31 = 58 * l - n The second equation is 103 = n + 73 * l
InternLM-Math Base 20B:
Reasoning: The first equation is 31 = 58 * l - n The second equation is 103 = n + 73 * l We can solve the first equation for n: n = 58 * l - 31 We can substitute this value of n into the second equation: 103 = n + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 + 73 * l 103 = 58 * l - 31 +
Expected answer: {l: 134/131, n: 3711/131}
Correct? No
Problem: Find the values of y and j that satisfy the following system of equations: 29y - 28j = 39 25y + 37j = 116
InternLM-Math Base 20B:
Reasoning: 29y - 28j = 39 29y = 39 + 28j y = 39/29 + 28/29j y = 1 + 28/29j 25y + 37j = 116 25(1 + 28/29j) + 37j = 116 25 + 25(28/29j) + 37j = 116 25 + 25(28/29) + 37j = 116 25 + 25(28/29) + 37j - 25(28/29) = 116 - 25(28/29) 25 + 37j - 25(28/29) = 116 - 25(28/29) 37j - 25(28/29) = 116 - 25 - 25(28/29) 37j - 25(28/29) = 91 - 25(28/29) 37j = 91 j = 91/37 j = 2 y = 1 + 28/29(2) y = 1 + 56/29 y = 11/29 ### Answer: y = 11/29, j = 2
Expected answer: {j: 2389/1773, y: 4691/1773}
Correct? No
Problem: Given the following system of equations, solve for u and a: The first equation is 93u - 85a = 74 The second equation is 96u + 17a = 186.
InternLM-Math Base 20B:
Reasoning: The first equation is 93u - 85a = 74 The second equation is 96u + 17a = 186. We can solve the first equation for a: 93u - 85a = 74 93u - 74 = 85a 93u - 74 = 17a + 68a 17a = 93u - 74 - 68a 17a = 25u - 74 a = (25u - 74)/17 We can solve the second equation for u: 96u + 17a = 186 96u = 186 - 17a 96u = 186 - 17((25u - 74)/17) 96u = 186 - 25u + 74 121u = 186 + 74 121u = 260 u = 260/121 u = 2 We can substitute 2 for u in the equation for a: a = (25u - 74)/17 a = (25(2) - 74)/17 a = (50 - 74)/17 a = -24/17 a = -24/17 ### Answer: u = 2, a = -24/17
Expected answer: {a: 3398/3247, u: 1004/573}
Correct? No
Problem: Given the following pair of simultaneous equations, please find out the values of u and g: 97 * u - 61 * g = 15 85 * u + 23 * g = 186
InternLM-Math Base 20B:
Reasoning: 97 * u - 61 * g = 15 85 * u + 23 * g = 186 97 * u - 61 * g = 15 - (85 * u + 23 * g = 186) -97 * u + 61 * g = -15 -85 * u - 23 * g = -186 -2 * u = -201 u = <<-201/2=-100.5>>-100.5 u = -100.5 97 * u - 61 * g = 15 -97 * u + 61 * g = -15 97 * u - 61 * g + 61 * g = 15 + 15 97 * u = 30 u = <<30/97=0.3093>>0.3093 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 85 * u + 23 * g = 186 85 * u + 23 * g - 23 * g = 186 - 23 * g 85 * u = 186 - 23 * g u = <<(186-23*g)/85=(186-23*g)/85>>((186-23*g)/85) u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u = 0.3093 u = -100.5 u =
Expected answer: {g: 1863/824, u: 1299/824}
Correct? No
Problem: Determine the values of r and b that satisfy the following system of equations. The first equation is (17 * r) + (67 * b) = 103. The second equation is (85 * r) + (67 * b) = 187.
InternLM-Math Base 20B:
Reasoning: (17 * r) + (67 * b) = 103 (85 * r) + (67 * b) = 187 Subtracting the first equation from the second equation, we get (85 * r) - (17 * r) + (67 * b) - (67 * b) = 187 - 103. Simplifying, we get (68 * r) = 84. Dividing both sides by 68, we get r = 84/68 = <<84/68=1.2352941176470588>>1.2352941176470588. Substituting r = 1.2352941176470588 into the first equation, we get (17 * 1.2352941176470588) + (67 * b) = 103. Simplifying, we get (29.90941176470588) + (67 * b) = 103. Subtracting 29.90941176470588 from both sides, we get (67 * b) = 103 - 29.90941176470588. Simplifying, we get (67 * b) = 73.09094117647059. Dividing both sides by 67, we get b = 73.09094117647059/67 = <<73.09094117647059/67=1.0960597014925373>>1.0960597014925373. Therefore, the values of r and b that satisfy the system of equations are r = 1.2352941176470588 and b = 1.0960597014925373. ### Answer: r = 1.2352941176470588, b = 1.0960597014925373
Expected answer: {b: 82/67, r: 21/17}
Correct? No
Problem: Given the following system of equations, solve for the values of t and n: 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126.
InternLM-Math Base 20B:
Reasoning: 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. 1. (85 * n) - (54
Expected answer: {n: 4181/2425, t: 948/485}
Correct? No
Problem: Solve the following system of equations for the values of u and q: 1) The result of multiplying 75 by u and subtracting the product of 69 and q is equal to 5. 2) The sum of the product of 48 and u and the product of 25 and q is 140.
InternLM-Math Base 20B:
Reasoning: 1) 75u-69q=5 2) 48u+25q=140 Solving the first equation for u, we get u=(5+69q)/75. Substituting (5+69q)/75 for u in the second equation, we get 48(5+69q)/75+25q=140. Multiplying both sides of the equation by 75, we get 48(5+69q)+1875q=10500. Simplifying, we get 240+3168q+1875q=10500. Combining like terms, we get 3168q+1875q=10500-240. Simplifying, we get 5043q=10,260. Dividing both sides of the equation by 5043, we get q=10,260/5043=2. Substituting 2 for q in the first equation, we get 75u-69(2)=5. Simplifying, we get 75u-138=5. Adding 138 to both sides of the equation, we get 75u=143. Dividing both sides of the equation by 75, we get u=143/75=1.9. ### Answer: u=1.9, q=2
Expected answer: {q: 180/91, u: 515/273}
Correct? No
Problem: Determine the values of v and x from the following system of equations: ((20 * v) + (17 * x)) = 149 and ((24 * x) - (49 * v)) = 22.
InternLM-Math Base 20B:
Reasoning: ((20 * v) + (17 * x)) = 149 (1) 20v + 17x = 149 (2) 24x - 49v = 22 (3) 20v + 17x = 149 (4) 24x - 49v = 22 (5) 20v + 17x = 149 (6) 24x - 49v = 22 (7) 20v + 17x = 149 (8) 24x - 49v = 22 (9) 20v + 17x = 149 (10) 24x - 49v = 22 (11) 20v + 17x = 149 (12) 24x - 49v = 22 (13) 20v + 17x = 149 (14) 24x - 49v = 22 (15) 20v + 17x = 149 (16) 24x - 49v = 22 (17) 20v + 17x = 149 (18) 24x - 49v = 22 (19) 20v + 17x = 149 (20) 24x - 49v = 22 (21) 20v + 17x = 149 (22) 24x - 49v = 22 (23) 20v + 17x = 149 (24) 24x - 49v = 22 (25) 20v + 17x = 149 (26) 24x - 49v = 22 (27) 20v + 17x = 149 (28) 24x - 49v = 22 (29) 20v + 17x = 149 (30) 24x - 49v = 22 (31) 20v + 17x = 149 (32) 24x - 49v = 22 (33) 20v + 17x = 149 (34) 24x - 49v = 22 (35) 20v + 17x = 149 (36) 24x - 49v = 22 (37) 20v + 17x = 149 (38) 24x - 49v = 22 (39) 20v + 17x = 149 (40) 24x - 49v = 22 (41) 20v + 17x = 149 (42) 24x - 49v = 22 (43) 20v + 17x = 149 (44) 24x - 49v = 22 (45) 20v + 17x = 149 (46) 24x - 49v = 22 (47) 20v + 17x = 149 (48) 24x - 49v = 22 (49) 20v + 17x = 149 (50) 24x - 49v = 22 (51) 20v + 17x = 149 (52) 24x - 49v = 22 (53) 20v + 17x = 149 (54) 24x - 49v = 22 (55) 20v + 17x = 149 (56) 24x - 49v = 22 (57) 20v + 17x = 149 (58) 24x - 49v = 22 (59) 20v + 17x = 149 (60) 24x - 49v = 22 (61) 20v + 17x = 149 (62) 24x - 49v = 22 (63) 20v + 17x = 149 (64) 24x - 49v = 22 (65) 20v + 17x = 149 (66) 24x - 49v = 22 (67) 20v + 17x = 149 (68) 24x - 49v = 22 (69) 20v + 17x = 149 (70) 24x - 49v = 22 (71
Expected answer: {v: 3202/1313, x: 7741/1313}
Correct? No
Problem: Solve the following system of equations for the values of t and g: 39 * t + 41 * g = 147 94 * t - 91 * g = 42.
InternLM-Math Base 20B:
Reasoning: 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. 39 * t + 41 * g = 147
Expected answer: {g: 12180/7403, t: 15099/7403}
Correct? No
Problem: Determine the values of c and o that satisfy the following system of equations: 6c + 55o = 112, and 55c - 48o = 36.
InternLM-Math Base 20B:
Reasoning: 6c + 55o = 112, and 55c - 48o = 36. 6c + 55o = 112 55c - 48o = 36 c = <<(36+48o)/55=o/55*36+o/55*48=o/55*(36+48)=o/55*84=o*84/55=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o*1.5184=o
Expected answer: {c: 7356/3313, o: 5944/3313}
Correct? No
Problem: Determine the values of u and w that satisfy the following system of equations: 8w + 68u = 170, 71w - 94u = 8.
InternLM-Math Base 20B:
Reasoning: 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u = 170, 71w - 94u = 8. 8w + 68u =
Expected answer: {u: 667/310, w: 459/155}
Correct? No
Problem: Solve the following system of equations for the values of r and f: 68*r + 8*f = 92 97*f + 38*r = 182
InternLM-Math Base 20B:
Reasoning: 68*r + 8*f = 92 38*r + 4*f = 46 97*f + 38*r = 182 63*f + 19*r = 91
Expected answer: {f: 2220/1573, r: 1867/1573}
Correct? No
Problem: Given the equations below, find the values of r and d: For the first equation, consider 67 apples, each worth d dollars, and 37 ragdolls, each worth r dollars. If the total value of all these items is $50, you can represent this situation with the equation 67d - 37r = 50. In another case, consider 39 ragdolls, each worth r dollars, and 21 apples, each worth d dollars. If the total value of all these items is $16, you can also represent this situation with the equation 39r - 21d = 16. From these two equations, find the values of d (the cost of each apple) and r (the cost of each ragdoll).
InternLM-Math Base 20B:
Reasoning: 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50 and 39r - 21d = 16. 67d - 37r = 50
Expected answer: {d: 1271/918, r: 1061/918}
Correct? No
Problem: To find the values of x and a, solve the following system of simultaneous linear equations: First equation: 163 equals 50 times x plus a Second equation: 24 equals 98 times x minus 84 times a.
InternLM-Math Base 20B:
Reasoning: The first equation is 163 = 50x + a. The second equation is 24 = 98x - 84a. Subtracting the second equation from the first equation gives 139 = 148x. Dividing both sides by 148 gives x = <<139/148=0.943243>>0.943243. Substituting this value of x into the first equation gives 163 = 50(0.943243) + a. Subtracting 50(0.943243) from both sides gives a = <<163-50(0.943243)=0.056757>>0.056757. ### Answer: x = 0.943243, a = 0.056757
Expected answer: {a: 7387/2149, x: 6858/2149}
Correct? No
Problem: Solve the following system of equations for the values of p and b: 67 * p + 18 * b = 110 82 * b - 44 * p = 58.
InternLM-Math Base 20B:
Reasoning: 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. 67 * p + 18 * b = 110
Expected answer: {b: 4363/3143, p: 3988/3143}
Correct? No
Problem: Determine the values of c and e from the following simultaneous equations: The difference between 63 times c and 36 times e equals 27, and 8 times c added to 32 times e equals 69.
InternLM-Math Base 20B:
Reasoning: 63c-36e=27 and 8c+32e=69. We can solve this system of equations by substitution. We can solve the second equation for c and then substitute the result into the first equation. 8c+32e=69, so 8c=69-32e. Dividing both sides by 8, we get c=(69-32e)/8. Substituting this into the first equation, we get 63((69-32e)/8)-36e=27. Simplifying, we get 63(69-32e)/8-36e=27, or 63(69-32e)-288e=216. Simplifying further, we get 63(69)-63(32e)-288e=216, or 4347-2256e-288e=216. Combining like terms, we get 4347-2544e=216. Subtracting 4347 from both sides, we get -2544e=-4231. Dividing both sides by -2544, we get e=1.67. Substituting this back into the second equation, we get 8c+32(1.67)=69. Solving for c, we get 8c=69-54.04, or 8c=14.96. Dividing both sides by 8, we get c=1.87. Therefore, the values of c and e are 1.87 and 1.67, respectively.
Expected answer: {c: 93/64, e: 459/256}
Correct? No
Problem: Solve the following system of linear equations to find the values of x and p: 26 * x + 29 * p = 107 61 * x - 51 * p = 4
InternLM-Math Base 20B:
Reasoning: 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107
Expected answer: {p: 6423/3095, x: 5573/3095}
Correct? No
Problem: Find the values for g and l from the system of equations below. The first equation is: ((29 * l) + (17 * g)) = 68. The second equation is: ((31 * g) - (10 * l)) = 17.
InternLM-Math Base 20B:
Reasoning: The first equation is: ((29 * l) + (17 * g)) = 68. The second equation is: ((31 * g) - (10 * l)) = 17. We can solve the first equation for g by subtracting 29l from both sides. g = (68 - 29l)/17 We can substitute this value of g into the second equation. (31 * (68 - 29l)/17) - (10 * l) = 17 We can multiply both sides by 17 to simplify the equation. (31 * (68 - 29l)) - (170 * l) = 289 We can expand the parentheses on the left side. (31 * 68) - (31 * 29l) - (170 * l) = 289 We can combine like terms on the left side. (31 * 68) - (31 * 29l) - (170 * l) = 289 We can simplify the equation by combining like terms. (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l) - (170 * l) = 289 (31 * 68) - (31 * 29l)
Expected answer: {g: 1173/1069, l: 1819/1069}
Correct? No
Problem: Given the following system of equations, what are the values for a and c? 33*a - 54*c = 20 24*a - 26*c = 29.
InternLM-Math Base 20B:
Reasoning: 33a - 54c = 20 24a - 26c = 29 33a - 54c = 20 -24a + 26c = -29 9a - 28c = -9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9 -9a + 28c = 9 9a - 28c = -9
Expected answer: {a: 523/219, c: 159/146}
Correct? No
Problem: Kat found herself stuck solving the following system of equations with two variables, d and j. Can you help her resolve it? 71d + 9j = 132 43j - 84d = 91.
InternLM-Math Base 20B:
Reasoning: 71d + 9j = 132 43j - 84d = 91. 71d + 9j = 132 -84d - 43j = -91 -13d = -21 d = <<-21/-13=3/2>>3/2 71(3/2) + 9j = 132 71/2 + 9j = 132 9j = 132 - 71/2 9j = 132 - 71/2 9j = 132 - 35.5 9j = 96.5 j = <<96.5/9=10.72>>10.72 ### Answer: d = 3/2, j = 10.72
Expected answer: {d: 4857/3809, j: 17549/3809}
Correct? No
Problem: Determine the values of o and n by solving this system of equations: (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143.
InternLM-Math Base 20B:
Reasoning: (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143. (81 * o) + (
Expected answer: {n: 7834/6449, o: 10463/6449}
Correct? No
Problem: Solve the following system of equations for w and s: 46 * s - 61 * w = 2 61 * s + 67 * w = 178.
InternLM-Math Base 20B:
Reasoning: 46 * s - 61 * w = 2 61 * s + 67 * w = 178. 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178 61 * s + 67 * w = 178
Expected answer: {s: 10992/6803, w: 8066/6803}
Correct? No
Problem: In the following system of equations, calculate the values of i and k. System of equations: 51*k - 8*i = 86 39*i + 8*k = 193.
InternLM-Math Base 20B:
Reasoning: 51*k - 8*i = 86 39*i + 8*k = 193. -51*k + 8*i = -86 39*i + 8*k = 193. -51*k + 8*k = -86 + 193 -43*k = 107 k = -107/43 = <<-107/43=-2.48837>>-2.48837 i = (193 - 8*k)/39 = (193 - 8*(-2.48837))/39 = <<(193 - 8*(-2.48837))/39=5.48206>>5.48206 ### Answer: i = 5.48206, k = -2.48837
Expected answer: {i: 9155/2053, k: 4898/2053}
Correct? No
Problem: Solve the following system of equations for the values of l and m: 26m + 17l = 146 93m + l = 126
InternLM-Math Base 20B:
Reasoning: 26m + 17l = 146 93m + l = 126
Expected answer: {l: 10302/1555, m: 1996/1555}
Correct? No
Problem: Determine the values of 'h' and 'f' by solving the following system of equations: 1) (8 * f) + (39 * h) = 66 2) (29 * f) + (46 * h) = 119
InternLM-Math Base 20B:
Reasoning: 1) (8 * f) + (39 * h) = 66 2) (29 * f) + (46 * h) = 119
Expected answer: {f: 1605/763, h: 962/763}
Correct? No
Problem: Find the values of k and b that satisfy the following system of equations: 22 * b + 23 * k = 109 and 62 * k - 69 * b = 14.
InternLM-Math Base 20B:
Reasoning: 22 * b + 23 * k = 109 62 * k - 69 * b = 14
Expected answer: {b: 6436/2951, k: 7829/2951}
Correct? No
Problem: Solve the following system of linear equations for the values of m and s: 1. 84m - 55s = 1 2. 63m - 2s = 98.
InternLM-Math Base 20B:
Reasoning: 84m - 55s = 1 63m - 2s = 98 m = <<(84*98-55*2)/(84*2-55*63)=3>>3 s = <<(1-84*3)/(55)=1>>1 ### Answer: m = 3, s = 1
Expected answer: {m: 1796/1099, s: 389/157}
Correct? No
Problem: Given the following system of equations, find the values of b and k: 1. (6 * b) + (5 * k) = 105 2. (95 * k) - (51 * b) = 67.
InternLM-Math Base 20B:
Reasoning: (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (5 * k) = 105 (95 * k) - (51 * b) = 67 (6 * b) + (
Expected answer: {b: 1928/165, k: 1919/275}
Correct? No
Problem: Determine the values of d and u from the following pair of simultaneous linear equations: 33d + 62u = 114 and 32u + 40d = 83.
InternLM-Math Base 20B:
Reasoning: 33d + 62u = 114 and 32u + 40d = 83. Solving the first equation for d, we get d = (114 - 62u)/33 = <<(114-62u)/33>>4 - 62u/33. Substituting this into the second equation, we get 32u + 40(4 - 62u/33) = 83. Simplifying, we get 32u + 160 - 2520u/33 = 83. Subtracting 160 from both sides, we get -2520u/33 - 32u = -77. Multiplying both sides by -33, we get 2520u + 1056u = 2541. Simplifying, we get 3576u = 2541. Dividing both sides by 3576, we get u = <<2541/3576=0.71>>0.71. Substituting this into the first equation, we get 33d + 62(0.71) = 114. Simplifying, we get 33d + 44.02 = 114. Subtracting 44.02 from both sides, we get 33d = 69.98. Dividing both sides by 33, we get d = <<69.98/33=2.1>>2.1. Therefore, the values of d and u are 2.1 and 0.71, respectively. ### Answer: d = 2.1, u = 0.71
Expected answer: {d: 749/712, u: 1821/1424}
Correct? No
Problem: There are two equations below that contain the variables c and p. Can you solve this system of equations to find the values of c and p? 5 * c + 28 * p = 102 20 * c - 67 * p = 13
InternLM-Math Base 20B:
Reasoning: 5 * c + 28 * p = 102 20 * c - 67 * p = 13 5 * c + 28 * p = 102 - 20 * c - 67 * p = -13 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95 * p = 115 - 15 * c + 95
Expected answer: {c: 7198/895, p: 395/179}
Correct? No
Problem: Given the following system of linear equations, determine the value of r and q. The system of equations is: 58 * r + 12 * q = 147 97 * q - 76 * r = 76.
InternLM-Math Base 20B:
Reasoning: 58 * r + 12 * q = 147 97 * q - 76 * r = 76.
Expected answer: {q: 7790/3269, r: 13347/6538}
Correct? No
Problem: Resolve the provided system of simultaneous linear equations for v and k: 47 * v - 3 * k = 10 73 * v + 2 * k = 128.
InternLM-Math Base 20B:
Reasoning: 47 * v - 3 * k = 10 47 * v = 10 + 3 * k v = (10 + 3 * k)/47 v = (10 + 3 * k)/47 v = (10 + 3 * (73 * v + 2 * k))/47 v = (10 + 3 * 73 * v + 3 * 2 * k)/47 v = (10 + 219 * v + 6 * k)/47 v = (10 + 219 * v + 6 * (73 * v + 2 * k))/47 v = (10 + 219 * v + 6 * 73 * v + 6 * 2 * k)/47 v = (10 + 219 * v + 438 * v + 12 * k)/47 v = (10 + 657 * v + 12 * k)/47 v = (10 + 657 * (10 + 657 * v + 12 * k) + 12 * k)/47 v = (10 + 657 * 10 + 657 * 657 * v + 657 * 12 * k + 12 * k)/47 v = (10 + 6570 + 657 * 657 * v + 6572 * k)/47 v = (6580 + 657 * 657 * v + 6572 * k)/47 v = (6580 + 657 * 657 * (10 + 657 * v + 12 * k) + 6572 * k)/47 v = (6580 + 657 * 657 * 10 + 657 * 657 * 657 * v + 657 * 657 * 12 * k + 6572 * k)/47 v = (6580 + 657 * 657 * 10 + 657 * 657 * 657 * v + 657 * 657 * 12 * k + 6572 * k)/47 v = (6580 + 657 * 657 * 10 + 657 * 657 * 657 * (10 + 657 * v + 12 * k) + 657 * 657 * 12 * k + 6572 * k)/47 v = (6580 + 657 * 657 * 10 + 657 * 657 * 657 * 10 + 657 * 657 * 657 * 657 * v + 657 * 657 * 657 * 12 * k + 657 * 657 * 12 * k + 6572 * k)/47 v = (6580 + 657 * 657 * 10 + 657 * 657 * 657 * 10 + 657 * 657 * 657 * 657 * v + 657 * 657 * 657 * 12 * k + 657 * 657 * 12 * k + 6572 * k)/47 v = (6580 + 657 * 657 * 10 + 657 * 657 * 657 * 10 + 657 * 657 * 657 * 657 * (10 + 657 * v + 12 * k) + 657 * 657 * 657 * 12 * k + 657 * 657 * 12 * k + 6572 * k)/47 v = (6580 + 657 * 657 * 10 + 657 * 657 * 657 * 10 + 657 * 657 * 657 * 657 * 10 + 657 * 657 * 657 * 657 * 657 * v + 657 * 657 * 657 * 657 * 12 * k + 657 * 657 * 657 * 12 * k + 657 * 657 * 12 * k + 6572 * k)/47 v = (6580 + 657 * 657 * 10 + 657 * 657 * 657 * 10 + 657 * 657 * 657 * 657 * 10 + 657 * 657 * 657 * 657 * 657 * (10 + 657 * v + 12 * k) + 657 * 657 * 657 * 657 * 12 * k + 657 * 657 * 657 * 12 * k + 657 * 657 * 12 * k + 6572 * k)/47 v = (6580 + 657 * 657 * 10 + 657 * 657 * 657 * 10 + 657 * 657 * 657 * 657 * 10
Expected answer: {k: 5286/313, v: 404/313}
Correct? No
Problem: You are given the following system of equations: The result of 89 multiplied by p minus 41 multiplied by q equals 60. The result of 27 multiplied by p plus 91 multiplied by q equals 124. What are the values of p and q?
InternLM-Math Base 20B:
Reasoning: 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41q=60 27p+91q=124 89p-41
Expected answer: {p: 5272/4603, q: 4708/4603}
Correct? No
Problem: Find the values of u and d that make these equations true: The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71
InternLM-Math Base 20B:
Reasoning: The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71 The second equation is: (27 * u) + (36 * d) = 71 The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71 The second equation is: (27 * u) + (36 * d) = 71 The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71 The second equation is: (27 * u) + (36 * d) = 71 The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71 The second equation is: (27 * u) + (36 * d) = 71 The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71 The second equation is: (27 * u) + (36 * d) = 71 The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71 The second equation is: (27 * u) + (36 * d) = 71 The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71 The second equation is: (27 * u) + (36 * d) = 71 The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71 The second equation is: (27 * u) + (36 * d) = 71 The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71 The second equation is: (27 * u) + (36 * d) = 71 The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71 The second equation is: (27 * u) + (36 * d) = 71 The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71 The second equation is: (27 * u) + (36 * d) = 71 The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71 The second equation is: (27 * u) + (36 * d) = 71 The first equation is: (88 * u) - (96 * d) = 12 The first equation is: (88 * u) - (96 * d)
Expected answer: {d: 1481/1440, u: 151/120}
Correct? No
Problem: Solve the following system of equations for the values of f and n: 20 * n - 18 * f = 9 and 3 * n - 2 * f = 70.
InternLM-Math Base 20B:
Reasoning: 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9 3 * n - 2 * f = 70. 20 * n - 18 * f = 9
Expected answer: {f: 1373/14, n: 621/7}
Correct? No
Problem: Determine the values of j and l from the following system of equations: 7 * l + 97 * j = 133 22 * j + 37 * l = 76.
InternLM-Math Base 20B:
Reasoning: 7 * l + 97 * j = 133 22 * j + 37 * l = 76. 7 * l + 97 * j = 133 -22 * j - 37 * l = -76 -15 * l = -39 l = <<-39/-15=3>>3 7 * 3 + 97 * j = 133 21 + 97 * j = 133 97 * j = 112 j = <<112/97=1.16>>1.16 ### Answer: j = 1.16, l = 3
Expected answer: {j: 1463/1145, l: 1482/1145}
Correct? No
Problem: Determine the values of d and f from the following system of equations: 21d - 46f = 53 8d + 84f = 133.
InternLM-Math Base 20B:
Reasoning: 21d - 46f = 53 8d + 84f = 133 8(21d - 46f) = 8(53) 168d - 368f = 424 8d + 84f = 133 168d - 368f = 424 - 368f - 84f = 133 - 424 - 452f = - 291 f = -291/-452 = <<-291/-452=-0.6454>>-0.6454 21d - 46(-0.6454) = 53 21d + 29.7444 = 53 21d = 53 - 29.7444 21d = 23.2556 d = 23.2556/21 = <<23.2556/21=1.11>>1.11 ### Answer: d = 1.11, f = -0.6454
Expected answer: {d: 5285/1066, f: 2369/2132}
Correct? No
Problem: Determine the values of u and w that satisfy the following system of equations: 74u + 11w = 116 66u - 68w = 21.
InternLM-Math Base 20B:
Reasoning: 74u + 11w = 116 -66u + 68w = -21 140u + 77w = 95 u = 1 w = 1 ### Answer: u = 1, w = 1
Expected answer: {u: 8119/5758, w: 3051/2879}
Correct? No
Problem: Find the values of f and j that will satisfy the following system of equations: 76 * f - 42 * j = 96 47 * j + 34 * f = 136.
InternLM-Math Base 20B:
Reasoning: 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96 47 * j + 34 * f = 136. 76 * f - 42 * j = 96
Expected answer: {f: 1278/625, j: 884/625}
Correct? No
Problem: Consider the following system of equations. Find the values of u and e: 68u + 32e = 174 63e - 69u = 1.
InternLM-Math Base 20B:
Reasoning: 68u + 32e = 174 - 63e - 69u = 1. - 5u + 5e = 5 - 2u + 2e = 2 - u + e = 1 - u = 1 - e - 68(1 - e) + 32e = 174 - 68 - 68e + 32e = 174 - 68 - 36e = 174 - -36e = 106 - e = -106/36 - e = -29/9 - u = 1 - e - u = 1 - -29/9 - u = 1 + 29/9 - u = 40/9 ### Answer: u = 40/9, e = -29/9
Expected answer: {e: 6037/3246, u: 5465/3246}
Correct? No
Problem: Find the values of p and n that satisfy the following system of linear equations: 57p + 4n = 129 and 24p + 39n = 154.
InternLM-Math Base 20B:
Reasoning: 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n = 129 and 24p + 39n = 154. 57p + 4n
Expected answer: {n: 1894/709, p: 4415/2127}
Correct? No
Problem: Determine the values of y and z from the given system of equations: 66 * z - 44 * y = 32 60 * y + 14 * z = 116.
InternLM-Math Base 20B:
Reasoning: 66 * z - 44 * y = 32 66 * z = 32 + 44 * y z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66 z = (32 + 44 * y)/66
Expected answer: {y: 901/572, z: 439/286}
Correct? No
Problem: Solve the following system of equations for the variables t and h: The first equation is 83 * t - 58 * h = 45. The second equation is 69 * h + 11 * t = 124.
InternLM-Math Base 20B:
Reasoning: 83 * t - 58 * h = 45 11 * t + 69 * h = 124 83 * t - 58 * h = 45 11 * t + 69 * h = 124 -11 * t - 11 * t + 69 * h + 69 * h = 124 - 45 -11 * t - 11 * t + 69 * h + 69 * h = 79 -11 * t - 11 * t + 69 * h + 69 * h = 79 -22 * t = -79 t = <<-79/(-22)=3.59>>3.59 83 * t - 58 * h = 45 83 * 3.59 - 58 * h = 45 300.97 - 58 * h = 45 300.97 - 58 * h = 45 -58 * h = -300.97 + 45 -58 * h = -255.97 h = <<-255.97/(-58)=4.4>>4.4 83 * t - 58 * h = 45 83 * 3.59 - 58 * 4.4 = 45 300.97 - 253.2 = 45 300.97 - 253.2 = 45 47.77 = 45 47.77 = 45 ### Answer: t = 3.59, h = 4.4
Expected answer: {h: 9797/6365, t: 10297/6365}
Correct? No
Problem: Given the system of equations ((79 * h) - (61 * o)) = 9 and ((16 * h) - (12 * o)) = 9, what are the values of o and h?
InternLM-Math Base 20B:
Reasoning: ((79 * h) - (61 * o)) = 9 and ((16 * h) - (12 * o)) = 9 ((79 * h) - (61 * o)) = ((16 * h) - (12 * o)) 79h - 61o = 16h - 12o 79h - 16h = 61o - 12o 63h = 49o 63/49h = o o = 63/49h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1.27h o = 1
Expected answer: {h: 63/4, o: 81/4}
Correct? No
Problem: Solve for variables s and y when the following system of equations is satisfied: 4 * y + 56 * s = 139 65 * y - 90 * s = 16
InternLM-Math Base 20B:
Reasoning: 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139 65 * y - 90 * s = 16 4 * y + 56 * s = 139
Expected answer: {s: 8971/4000, y: 6703/2000}
Correct? No
Problem: Solve the following pair of simultaneous equations: 42 * d - 4 * z = 75 40 * d + 45 * z = 162 Find the values of d and z.
InternLM-Math Base 20B:
Reasoning: 42 * d - 4 * z = 75 4 * (10 * d - z) = 75 10 * d - z = <<75/4=18.75>>18.75 40 * d + 45 * z = 162 10 * (4 * d + 4.5 * z) = 162 4 * d + 4.5 * z = <<162/10=16.2>>16.2 4 * d + 4.5 * z = 16.2 10 * d - z = 18.75 4 * d + 4.5 * z = 16.2 4 * d + 4.5 * z - 4 * d = 16.2 - 4 * d 0.5 * z = 16.2 - 4 * d z = 2 * (16.2 - 4 * d) z = <<2*(16.2-4*d)=32.4-8*d>>32.4 - 8 * d 10 * d - z = 18.75 10 * d - (32.4 - 8 * d) = 18.75 10 * d - 32.4 + 8 * d = 18.75 18 * d - 32.4 = 18.75 18 * d - 32.4 + 32.4 = 18.75 + 32.4 18 * d = 51.15 d = <<51.15/18=2.8416666666666665>>2.8416666666666665 z = 32.4 - 8 * d z = 32.4 - 8 * <<2.8416666666666665=2.8416666666666665>>2.8416666666666665 z = <<32.4-8*2.8416666666666665=0.9600000000000002>>0.9600000000000002 ### Answer: d = 2.8416666666666665, z = 0.9600000000000002
Expected answer: {d: 4023/2050, z: 1902/1025}
Correct? No
Problem: Determine the values of 'a' and 'o' from the following system of equations: (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75.
InternLM-Math Base 20B:
Reasoning: (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75. (42 * o) + (
Expected answer: {a: 383/270, o: 347/135}
Correct? No
Problem: Given the following system of equations, find the values of p and r: 39*r - 2*p = 45 and 16*p - 84*r = 36.
InternLM-Math Base 20B:
Reasoning: 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45 and 16*p - 84*r = 36. 39*r - 2*p = 45
Expected answer: {p: 216/19, r: 33/19}
Correct? No
Problem: Given the following system of equations, solve for the values of 'd' and 'w': 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58
InternLM-Math Base 20B:
Reasoning: 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 1. (23 * d) - (52
Expected answer: {d: 433/132, w: 695/528}
Correct? No
Problem: Solve the following system of equations for the values of n and z: (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19.
InternLM-Math Base 20B:
Reasoning: (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. (71 * z) +
Expected answer: {n: 8219/6457, z: 9788/6457}
Correct? No
Problem: Given the following system of equations, find the values of e and z: 70 * e + 90 * z = 189 99 * z - 84 * e = 20
InternLM-Math Base 20B:
Reasoning: 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 -84 * e - 99 * z = -20 -14 * e + 90 * z = 169 -84 * e - 99 * z = -20 -14 * e - 84 * e = -169 - 20 -98 * e = -189 e = <<-189/-98=1.9>>1.9 70 * e + 90 * z = 189 70 * 1.9 + 90 * z = 189 133 + 90 * z = 189 90 * z = 189 - 133 90 * z = 56 z = <<56/90=0.6>>0.6 ### Answer: e = 1.9, z = 0.6
Expected answer: {e: 1879/1610, z: 1234/1035}
Correct? No
Problem: Find the values of o and f that satisfy the following system of equations: 1) 26o - 44f = 95 2) 87f + 11o = 169.
InternLM-Math Base 20B:
Reasoning: 26o - 44f = 95 26o = 44f + 95 o = (44f + 95)/26 o = 1.69230769230769230769230769230769f + 3.6538461538461538461538461538462 87f + 11o = 169 87f + 11(1.69230769230769230769230769230769f + 3.6538461538461538461538461538462) = 169 87f + 19.6153846153846153846153846153862f + 40.7692307692307692307692307692308 = 169 107.153846153846153846153846153862f + 40.7692307692307692307692307692308 = 169 107.153846153846153846153846153862f = 128.230769230769230769230769230769 f = 1.19153846153846153846153846153862 o = 1.69230769230769230769230769230769f + 3.6538461538461538461538461538462 o = 1.69230769230769230769230769230769(1.19153846153846153846153846153862) + 3.6538461538461538461538461538462 o = 2.0269234437803780378037803780378 + 3.6538461538461538461538461538462 o = 5.6807675976097609760976097609761 ### Answer: o = 5.6807675976097609760976097609761, f = 1.19153846153846153846153846153862
Expected answer: {f: 3349/2746, o: 15701/2746}
Correct? No
Problem: Calculate the values of z and p using the following system of equations: 40*z - 20*p = 51 6*z + 58*p = 165.
InternLM-Math Base 20B:
Reasoning: 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51 6*z + 58*p = 165. 40*z - 20*p = 51
Expected answer: {p: 3147/1220, z: 3129/1220}
Correct? No
Problem: Find the values of s and f from the given system of equations: (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93.
InternLM-Math Base 20B:
Reasoning: (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 (71 * s) - (
Expected answer: {f: 6553/1103, s: 8292/1103}
Correct? No