DeepSeek Math 7B Base 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
DeepSeek Math 7B Base:
Reasoning: 1. (40 * s) - (91 * q) = 37 2. (30 * s) + (12 * q) = 121 Multiply the first equation by 3 and the second equation by 4. 1. (120 * s) - (273 * q) = 111 2. (120 * s) + (48 * q) = 484 Subtract the second equation from the first equation. -321 * q = -373 Divide both sides by -321. q = 1.1617977528089887640449438202247 Substitute q = 1.1617977528089887640449438202247 into the first equation. (40 * s) - (91 * 1.1617977528089887640449438202247) = 37 Simplify. (40 * s) - 105.71268502179989868400442481782 = 37 Add 105.71268502179989868400442481782 to both sides. (40 * s) = 142.71268502179989868400442481782 Divide both sides by 40. s = 3.5678171255449974671001106204455 ### Answer: q = 1.1617977528089887640449438202247, s = 3.5678171255449974671001106204455
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.
DeepSeek Math 7B Base:
Reasoning: 4 * b + 44 * m = 180 and 79 * m - 6 * b = 48. 4 * b + 44 * m = 180 4 * b = 180 - 44 * m b = (180 - 44 * m) / 4 79 * m - 6 * b = 48 79 * m - 6 * (180 - 44 * m) / 4 = 48 79 * m - 6 * (180 - 44 * m) = 48 * 4 79 * m - 6 * 180 + 6 * 44 * m = 192 79 * m - 1080 + 264 * m = 192 343 * m = 192 + 1080 343 * m = 1272 m = 1272 / 343 b = (180 - 44 * m) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 * (1272 / 343)) / 4 b = (180 - 44 *
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.
DeepSeek Math 7B Base:
Reasoning: 42 * o - 15 * g = 28 47 * o + 29 * g = 141. Multiply the first equation by 29 and the second equation by 15. 1218 * o - 435 * g = 792 705 * o + 435 * g = 2115. Add the two equations. 1923 * o = 2907. Divide both sides by 1923. o = 1.51. Substitute o = 1.51 into the first equation. 42 * 1.51 - 15 * g = 28. 63.42 - 15 * g = 28. Subtract 63.42 from both sides. -15 * g = -35.42. Divide both sides by -15. g = 2.36. ### Answer: o = 1.51, g = 2.36.
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. We can solve for v in the first equation: v = (21 + 6 * o) / 12. We can substitute this expression for v into the second equation: 76 * ((21 + 6 * o) / 12) - 45 * o = 50. Simplifying this equation, we get: 152 + 30 * o - 45 * o = 50. Simplifying further, we get: 152 - 15 * o = 50. Solving for o, we get: o = (152 - 50) / 15 = 6.8. Substituting this value of o into the first equation, we get: 12 * v - 6 * 6.8 = 21. Simplifying this equation, we get: 12 * v - 40.8 = 21. Solving for v, we get: v = (21 + 40.8) / 12 = 4.3. ### Answer: v = 4.3, o = 6.8
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.
DeepSeek Math 7B Base:
Reasoning: 75 * f + 25 * g = 138 and 2 * f + 90 * g = 143. Multiply the first equation by 2: 150 * f + 50 * g = 276. Subtract the second equation from the first: 148 * f = 133. Divide both sides by 148: f = 133/148. Substitute f = 133/148 into the first equation: 75 * 133/148 + 25 * g = 138. Simplify: 25 * g = 138 - 75 * 133/148. Solve for g: g = (138 - 75 * 133/148) / 25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/25 - 75 * 133/148/25. Simplify: g = 138/
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. We can solve for y in the first equation: y = (194 - 14 * n) / 4. We can then substitute this value for y into the second equation: 7 = 65 * n - 79 * ((194 - 14 * n) / 4). We can then solve for n: 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * n - 79 * ((194 - 14 * n) / 4) 7 = 65 * 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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. First, we can solve the first equation for g: 146 = 28 * g + 26 * l 146 - 26 * l = 28 * g (146 - 26 * l) / 28 = g Now, we can substitute this expression for g into the second equation: 6 = 41 * l - 53 * g 6 = 41 * l - 53 * ((146 - 26 * l) / 28) 6 = 41 * l - (53 * (146 - 26 * l)) / 28 6 = (41 * l * 28 - 53 * (146 - 26 * l)) / 28 6 * 28 = 41 * l * 28 - 53 * (146 - 26 * l) 168 = 41 * l * 28 - 53 * (146 - 26 * l) Now, we can solve for l: 168 = 41 * l * 28 - 53 * (146 - 26 * l) 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l * 28 - 53 * 146 + 53 * 26 * l 168 = 41 * l
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 1) 20 * p + 56 * y = 90 2) 89 * p + 7 * y = 98 From equation 2), we can solve for p in terms of y: p = (98 - 7y) / 89 Substituting this expression for p into equation 1), we get: 20 * (98 - 7y) / 89 + 56 * y = 90 Simplifying, we get: 1960 - 140y + 56y = 8010 Solving for y, we get: y = (1960 - 8010) / (-140 + 56) = 10 Substituting this value of y into the expression for p, we get: p = (98 - 7 * 10) / 89 = 1 Therefore, the solution to the system of equations is p = 1 and y = 10. ### Answer: p = 1 and y = 10
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.
DeepSeek Math 7B Base:
Reasoning: 72*k - 22*d = 17 and 6*d +69*k = 96 72*k - 22*d = 17 72*k = 17 + 22*d k = (17 + 22*d)/72 6*d +69*k = 96 6*d +69*(17 + 22*d)/72 = 96 6*d + (69*17 + 69*22*d)/72 = 96 6*d + (1173 + 1518*d)/72 = 96 6*d*72 + 1173 + 1518*d = 96*72 432*d + 1173 + 1518*d = 96*72 1950*d + 1173 = 96*72 1950*d = 96*72 - 1173 1950*d = 6912 - 1173 1950*d = 5739 d = 5739/1950 d = 1913/650 k = (17 + 22*d)/72 k = (17 + 22*(1913/650))/72 k = (17 + 42086/650)/72 k = (17*650 + 42086/650)/72 k = (11050 + 42086/650)/72 k = (11050 + 67)/72 k = 11117/72 ### Answer: k = 11117/72 and d = 1913/650
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
DeepSeek Math 7B Base:
Reasoning: 73 * h - 33 * d = 48 10 * d + 14 * h = 91 Multiply the first equation by 10 and the second equation by 33 to get: 730 * h - 330 * d = 480 330 * d + 462 * h = 2967 Add the two equations to get: 1192 * h = 3447 Divide both sides by 1192 to get: h = 2.900921659 Substitute the value of h into the first equation to get: 73 * 2.900921659 - 33 * d = 48 Multiply both sides by 10 to get: 730 * 2.900921659 - 330 * d = 480 Subtract 2119.666667 from both sides to get: -330 * d = -1219.666667 Divide both sides by -330 to get: d = 3.701717171 ### Answer: d = 3.701717171, h = 2.900921659
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
DeepSeek Math 7B Base:
Reasoning: 1) 43 * q - 44 * e = 29 2) 30 * q + 43 * e = 130 Multiply the first equation by 43 and the second equation by 44. 1) 43 * 43 * q - 44 * 43 * e = 29 * 43 2) 30 * 44 * q + 43 * 44 * e = 130 * 44 Simplify the equations. 1) 1849 * q - 1892 * e = 1247 2) 1320 * q + 1892 * e = 5720 Add the two equations. 1849 * q + 1320 * q = 1247 + 5720 Simplify the equation. 3169 * q = 6967 Divide both sides of the equation by 3169. q = 6967/3169 Substitute the value of q into the first equation. 43 * 6967/3169 - 44 * e = 29 Simplify the equation. 295471/3169 - 44 * e = 29 Subtract 295471/3169 from both sides of the equation. -44 * e = 29 - 295471/3169 Simplify the equation. -44 * e = 1000/3169 Divide both sides of the equation by -44. e = -1000/3169 / -44 Simplify the equation. e = 250/3169 ### Answer: q = 6967/3169, e = 250/3169
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))
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. From the second equation, we can solve for a: 109 = ((37 * a) + (6 * r)) 109 - (6 * r) = (37 * a) (109 - (6 * r)) / 37 = a Substituting this expression for a into the first equation, we get: 53 = ((89 * r) - (74 * ((109 - (6 * r)) / 37))) 53 = ((89 * r) - (74 * (109 - (6 * r)) / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89 * r) - (74 * 109 / 37) + (74 * 6 * r / 37)) 53 = ((89
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.
DeepSeek Math 7B Base:
Reasoning: 1. 42g + 12q = 169 2. 12q - 50g = 19 Solving for 'g' and 'q' using the substitution method: 1. 42g + 12q = 169 2. 12q - 50g = 19 From equation 2, we can solve for 'q' in terms of 'g': 1. 42g + 12q = 169 2. 12q - 50g = 19 3. 12q = 19 + 50g 4. q = (19 + 50g) / 12 Substituting 'q' in equation 1: 1. 42g + 12q = 169 2. 12q - 50g = 19 3. 42g + 12(19 + 50g) / 12 = 169 4. 42g + 19 + 50g = 169 5. 92g = 150 6. g = 150/92 Substituting 'g' in equation 2: 1. 42g + 12q = 169 2. 12q - 50g = 19 3. 12q - 50(150/92) = 19 4. 12q = 19 + 50(150/92) 5. q = (19 + 50(150/92)) / 12 ### Answer: 1. g = 150/92 2. q = (19 + 50(150/92)) / 12
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
DeepSeek Math 7B Base:
Solving the first equation for s, we get: s = (54 + 11 * v) / 37 Substituting this into the second equation, we get: 82 * (54 + 11 * v) / 37 - 62 * v = 41 Simplifying, we get: (4428 + 908 * v) / 37 - 62 * v = 41 Multiplying both sides by 37, we get: 4428 + 908 * v - 2278 * v = 1517 Simplifying, we get: -1370 * v = -2911 Dividing both sides by -1370, we get: v = 2.124657534246575 Substituting this into the first equation, we get: s = (54 + 11 * 2.124657534246575) / 37 Simplifying, we get: s = 1.624657534246575 ### Answer: s = 1.624657534246575, v = 2.124657534246575
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the elimination method. Multiply the first equation by 48 and the second equation by 65 to get: 48 * (41 * c + 65 * z) = 48 * 151 65 * (78 * z - 48 * c) = 65 * 48 Simplifying the equations, we get: 2,016 * c + 3,120 * z = 7,248 5,130 * z - 3,120 * c = 3,120 Adding the two equations, we get: 2,016 * c + 5,130 * z = 10,368 Solving for z, we get: z = 10,368 / (2,016 + 5,130) z = 10,368 / 7,146 z = 1.45 Substituting z = 1.45 into the first equation, we get: 41 * c + 65 * 1.45 = 151 41 * c + 93.25 = 151 41 * c = 151 - 93.25 41 * c = 57.75 c = 57.75 / 41 c = 1.41 ### Answer: c = 1.41, z = 1.45
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?
DeepSeek Math 7B Base:
Reasoning: 60 * c - 91 * i = 7 7 * i + 76 * c = 148 Multiply the first equation by 7 and the second equation by 91. 420 * c - 637 * i = 49 6447 * i + 6844 * c = 13558 Subtract the first equation from the second equation. 6405 * i + 6801 * c = 13510 Divide both sides by 6405. i + 1.0625 * c = 2.1091 Subtract 1.0625 * c from both sides. i = 2.1091 - 1.0625 * c Substitute 2.1091 - 1.0625 * c for i in the first equation. 60 * c - 91 * (2.1091 - 1.0625 * c) = 7 Simplify. 60 * c - 191.1919 + 96.1875 * c = 7 Add 191.1919 to both sides. 156.1875 * c = 208.1919 Divide both sides by 156.1875. c = 1.3333 Substitute 1.3333 for c in the first equation. 60 * 1.3333 - 91 * i = 7 Simplify. 79.998 - 91 * i = 7 Subtract 79.998 from both sides. -91 * i = -72.998 Divide both sides by -91. i = 0.7999 ### Answer: c = 1.3333, i = 0.7999
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
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 1) 71*v - 37*e = 69 2) 41*e + 76*v = 184 From equation 1, we can solve for e: e = (71*v - 69) / 37 Substituting this expression for e into equation 2, we get: 41*((71*v - 69) / 37) + 76*v = 184 Simplifying this equation, we get: (2911*v - 2871) / 37 + 76*v = 184 Multiplying both sides by 37, we get: 2911*v - 2871 + 2812*v = 6724 Simplifying this equation, we get: 5723*v = 9595 Dividing both sides by 5723, we get: v = 1.6785 Substituting this value for v into the expression for e, we get: e = (71*1.6785 - 69) / 37 Simplifying this expression, we get: e = 0.3215 ### Answer: e = 0.3215, v = 1.6785
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.
DeepSeek Math 7B Base:
Reasoning: 25v+69d=113 26d+42v=85 We can solve this system of equations by using the substitution method. First, we can solve for 'v' in the first equation: v = (113-69d)/25 Then, we can substitute this value for 'v' into the second equation: 26d+42((113-69d)/25) = 85 Simplifying this equation, we get: 26d+42((113-69d)/25) = 85 26d+42(113-69d)/25 = 85 26d+42(113-69d) = 85*25 26d+4806-2874d = 2125 -2618d = -2681 d = 1.0265 Now, we can substitute this value for 'd' into the first equation to solve for 'v': 25v+69(1.0265) = 113 25v+70.8735 = 113 25v = 42.1265 v = 1.68506 ### Answer: d=1.0265, v=1.68506
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
DeepSeek Math 7B Base:
Reasoning: 43 * z - 91 * g = 33 72 * g - 3 * z = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z - 91 * g = 33 -3 * z + 72 * g = 68 43 * z
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.
DeepSeek Math 7B Base:
Reasoning: 50c + 12f = 92 36c - 21f = 34. Multiply the first equation by 3 and the second equation by 5. 150c + 36f = 276 180c - 105f = 170. Subtract the second equation from the first. -30c + 141f = 106. Divide both sides by 30. -c + 4.7f = 3.53. Add c to both sides. 4.7f = c + 3.53. Subtract 3.53 from both sides. 4.7f - 3.53 = c. Substitute 4.7f - 3.53 for c in the first equation. 50(4.7f - 3.53) + 12f = 92. Multiply. 235f - 176.5 + 12f = 92. Add 176.5 to both sides. 247f = 268.5. Divide both sides by 247. f = 1.09. Substitute 1.09 for f in the first equation. 50c + 12(1.09) = 92. Multiply. 50c + 12.96 = 92. Subtract 12.96 from both sides. 50c = 79.04. Divide both sides by 50. c = 1.58. ### Answer: c = 1.58, f = 1.09.
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
DeepSeek Math 7B Base:
The first step is to solve for one of the variables in one of the equations. Let's solve for u in the first equation. 1) 87u - 75d = 7 87u = 7 + 75d u = (7 + 75d) / 87 Now that we have an expression for u, we can substitute it into the second equation: 2) 85d - 82u = 54 85d - 82((7 + 75d) / 87) = 54 85d - (82(7 + 75d)) / 87 = 54 85d - (574 + 6300d) / 87 = 54 85d - 574/87 - 6300d/87 = 54 (85d - 574/87 - 6300d/87) * 87 = 54 * 87 85d * 87 - 574 - 6300d = 4758 7095d - 574 = 4758 7095d = 4758 + 574 7095d = 5332 d = 5332/7095 Now that we have an expression for d, we can substitute it into the first equation: 1) 87u - 75d = 7 87u - 75(5332/7095) = 7 87u - 399900/7095 = 7 87u - 399900/7095 = 7 87u = 7 + 399900/7095 87u = (7 * 7095 + 399900) / 7095 87u = (49665 + 399900) / 7095 87u = 449565/7095 u = 449565/(7095 * 87) u = 449565/618465 u = 1/13 So the values of u and d are u = 1/13 and d = 5332/7095. ### Answer: u = 1/13 and d = 5332/7095
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?
DeepSeek Math 7B Base:
Reasoning: We can solve for i in the first equation: (75 * a) - (4 * i) = 42 (4 * i) = (75 * a) - 42 i = (75 * a - 42) / 4 We can then substitute this value of i into the second equation: (10 * i) + (13 * a) = 160 (10 * (75 * a - 42) / 4) + (13 * a) = 160 (750 * a - 420) / 4 + (13 * a) = 160 (750 * a - 420) + (52 * a) = 640 750 * a + 52 * a = 640 + 420 802 * a = 1060 a = 1060 / 802 a = 1.3217821782178217821782178217822 We can then substitute this value of a into the first equation to solve for i: (75 * a) - (4 * i) = 42 (75 * 1.3217821782178217821782178217822) - (4 * i) = 42 100.63366336633663366336633663366 - (4 * i) = 42 4 * i = 100.63366336633663366336633663366 - 42 4 * i = 58.633663366336633663366336633663 i = 58.633663366336633663366336633663 / 4 i = 14.658415841584158415841584158416 ### Answer: i = 14.658415841584158415841584158416, a = 1.3217821782178217821782178217822
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
DeepSeek Math 7B Base:
Reasoning: 37 * p + 74 * c = 183 27 * c - 18 * p = 13 Multiply the first equation by 2 and the second equation by 37: 74 * p + 148 * c = 366 979 * c - 666 * p = 481 Add the two equations: 1053 * c = 847 Divide both sides by 1053: c = 847/1053 Substitute the value of c into the first equation: 37 * p + 74 * (847/1053) = 183 Multiply both sides by 1053: 37 * p + 62258 = 191721 Subtract 62258 from both sides: 37 * p = 129463 Divide both sides by 37: p = 129463/37 ### Answer: p = 129463/37, c = 847/1053
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.
DeepSeek Math 7B Base:
Reasoning: (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. Multiply the first equation by 33 and the second equation by 30. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (1584 * k) - (990 * p) = 1221 (480 * p) + (999 * k) = 3150. Subtract the first equation from the second equation. (1584 * k) - (990 * p) = 1221 (480 * p) + (999 * k) = 3150. (1104 * k) - (1470 * p) = 1929. Divide both sides by 1104. (1104 * k) - (1470 * p) = 1929. k - (1470/1104 * p) = 1929/1104. k = 1929/1104 + (1470/1104 * p). Substitute the value of k into the first equation. (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * (1929/1104 + (1470/1104 * p))) - (30 * p) = 37 (16 * p) + (33 * k) = 105. (48 * (1929/1104 + (1470/1104 * p))) - (30 * p) = 37 (16 * p) + (33 * (1929/1104 + (1470/1104 * p))) = 105. (48 * (1929/1104 + (1470/1104 * p))) - (30 * p) = 37 (16 * p) + (33 * (1929/1104 + (1470/1104 * p))) = 105. (48 * (1929/1104 + (1470/1104 * p))) - (30 * p) = 37 (16 * p) + (33 * (1929/1104 + (1470/1104 * p))) = 105. (48 * (1929/1104 + (1470/1104 * p))) - (30 * p) = 37 (16 * p) + (33 * (1929/1104 + (1470/1104 * p))) = 105. (48 * (1929/1104 + (1470/1104 * p))) - (30 * p) = 37 (16 * p) + (33 * (1929/1104 + (1470/1104 * p))) = 105. (48 * (1929/1104 + (1470/1104 * p))) - (30 * p) = 37 (16 * p) + (33 * (1929/1104 + (1470/1104 * p))) = 105. (48 * (1929/1104 + (1470/1104 * p))) - (30 * p) = 37 (16 * p) + (33 * (1929/1104 + (1470/1104 * p))) = 10
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the elimination method. Multiply the first equation by 46 and the second equation by 75. 1. 3450v - 3204f = 644 2. 3450v + 3975f = 8250 Subtract the first equation from the second equation. 3975f - 3204f = 8250 - 644 771f = 7606 f = 7606/771 f = <<7606/771=9.87>>9.87 Substitute the value of f into the first equation. 75v - 69(9.87) = 14 75v - 680.43 = 14 75v = 694.43 v = 694.43/75 v = <<694.43/75=9.26>>9.26 ### Answer: v = 9.26, f = 9.87
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.
DeepSeek Math 7B Base:
Reasoning: 7 * o + 13 * g = 131 89 * g - 70 * o = 37. Multiply the first equation by 70 and the second equation by 7 to get: 490 * o + 910 * g = 9170 623 * g - 490 * o = 259. Add the two equations to get: 1533 * g = 9429. Divide both sides by 1533 to get: g = 6.14. Substitute g = 6.14 into the first equation to get: 7 * o + 13 * 6.14 = 131. Simplify to get: 7 * o + 79.82 = 131. Subtract 79.82 from both sides to get: 7 * o = 51.18. Divide both sides by 7 to get: o = 7.31. ### Answer: o = 7.31, g = 6.14.
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the elimination method. Multiply the first equation by 3 and the second equation by 8 to get: 264 * d - 180 * k = 114 264 * k - 88 * d = 368. Add the two equations to get: 264 * d - 180 * k + 264 * k - 88 * d = 114 + 368 176 * d = 482 d = 482/176 = <<482/176=2.74>>2.74. Substitute d = 2.74 into the first equation to get: 88 * 2.74 - 60 * k = 38 240.32 - 60 * k = 38 -60 * k = 38 - 240.32 = -202.32 k = -202.32/-60 = <<-202.32/-60=3.37>>3.37. ### Answer: d = 2.74, k = 3.37
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.
DeepSeek Math 7B Base:
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
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. From the second equation, we can solve for v: v = (91 - 30 * o) / 8. Substituting this expression for v into the first equation, we get: (87 * o) - (29 * (91 - 30 * o) / 8) = 1. Simplifying this equation, we get: (87 * o) - (29 * 91 / 8) + (29 * 30 * o / 8) = 1. Simplifying further, we get: (87 * o) + (29 * 30 * o / 8) = 1 + (29 * 91 / 8). Simplifying this equation, we get: (87 * o) + (29 * 30 * o / 8) = (8 * 1 + 29 * 91) / 8. Simplifying further, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying this equation, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying further, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying this equation, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying further, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying this equation, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying further, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying this equation, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying further, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying this equation, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying further, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying this equation, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying further, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying this equation, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying further, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying this equation, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying further, we get: (87 * o) + (29 * 30 * o / 8) = (8 + 29 * 91) / 8. Simplifying this equation, we get: (87 * o) + (29 *
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. First, we can solve the first equation for h: (23 * h) - (46 * p) = 58 23h = 58 + 46p h = (58 + 46p) / 23 Now, we can substitute this expression for h into the second equation: (11 * p) + (23 * h) = 124 (11 * p) + (23 * (58 + 46p) / 23) = 124 11p + 58 + 46p = 124 57p = 66 p = 66/57 Now, we can substitute this value for p into the expression for h: h = (58 + 46p) / 23 h = (58 + 46(66/57)) / 23 h = (58 + 524/19) / 23 h = (1106/19) / 23 h = 1106/437 Therefore, the solution to the system of equations is h = 1106/437 and p = 66/57. ### Answer: h = 1106/437 and p = 66/57
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.
DeepSeek Math 7B Base:
Reasoning: 1) 19d + 6f = 120, 2) 90d - 42f = 69. Multiply the first equation by 3 to get 57d + 18f = 360. Multiply the second equation by 2 to get 180d - 84f = 138. Subtract the second equation from the first equation to get 123d = 222. Divide both sides by 123 to get d = 1.8. Substitute d = 1.8 into the first equation to get 19(1.8) + 6f = 120. Simplify to get 34.2 + 6f = 120. Subtract 34.2 from both sides to get 6f = 85.8. Divide both sides by 6 to get f = 14.3. ### Answer: d = 1.8, f = 14.3
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'?
DeepSeek Math 7B Base:
Reasoning: We can solve this system of linear equations by using the substitution method. From equation 1, we can solve for 'm' in terms of 'r': m = (127 - 55r) / 42 Substituting this expression for 'm' into equation 2, we get: 66 * (127 - 55r) / 42 - 52r = 44 Simplifying this equation, we get: -100r + 127 = 44 Solving for 'r', we get: r = 83/100 Substituting this value of 'r' into the expression for 'm' in terms of 'r', we get: m = (127 - 55 * 83/100) / 42 Simplifying this expression, we get: m = 11/100 Therefore, the solution to the system of linear equations is: r = 83/100 m = 11/100 ### Answer: r = 83/100, m = 11/100
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
DeepSeek Math 7B Base:
Reasoning: We can solve this system of linear equations by using the substitution method. First, we can solve for n in the first equation: 31n + 64w = 120 31n = 120 - 64w n = (120 - 64w) / 31 Next, we can substitute this expression for n into the second equation: 57w + 71n = 173 57w + 71((120 - 64w) / 31) = 173 57w + 71(120 - 64w) / 31 = 173 Multiplying both sides by 31: 1767w + 71(120 - 64w) = 5363 1767w + 8520 - 4544w = 5363 -1877w + 8520 = 5363 -1877w = 5363 - 8520 -1877w = -3157 w = -3157 / -1877 w = 1.68 Now, we can substitute this value of w into the first equation to find the value of n: 31n + 64w = 120 31n + 64(1.68) = 120 31n + 106.08 = 120 31n = 120 - 106.08 31n = 13.92 n = 13.92 / 31 n = 0.45 Therefore, the values of n and w that satisfy the system of linear equations are n = 0.45 and w = 1.68. ### Answer: n = 0.45, w = 1.68
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.
DeepSeek Math 7B Base:
Reasoning: 1) 72 * a + 26 * u = 112 2) 76 * u - 77 * a = 31. Multiply the first equation by 77 and the second equation by 26. 1) 72 * 77 * a + 26 * 77 * u = 112 * 77 2) 76 * 26 * u - 77 * 26 * a = 31 * 26. Add the two equations. 72 * 77 * a + 76 * 26 * u - 77 * 26 * a = 112 * 77 + 31 * 26. Simplify. 72 * 77 * a - 77 * 26 * a + 76 * 26 * u = 112 * 77 + 31 * 26. Factor out a. a * (72 * 77 - 77 * 26) + 76 * 26 * u = 112 * 77 + 31 * 26. Simplify. a * 3080 + 76 * 26 * u = 112 * 77 + 31 * 26. Divide both sides by 3080. a + 76 * 26 * u / 3080 = 112 * 77 / 3080 + 31 * 26 / 3080. Simplify. a + 76 * 26 * u / 3080 = 112 * 77 / 3080 + 31 * 26 / 3080. Simplify. a + 76 * 26 * u / 3080 = 112 * 77 / 3080 + 31 * 26 / 3080. Simplify. a + 76 * 26 * u / 3080 = 112 * 77 / 3080 + 31 * 26 / 3080. Simplify. a + 76 * 26 * u / 3080 = 112 * 77 / 3080 + 31 * 26 / 3080. Simplify. a + 76 * 26 * u / 3080 = 112 * 77 / 3080 + 31 * 26 / 3080. Simplify. a + 76 * 26 * u / 3080 = 112 * 77 / 3080 + 31 * 26 / 3080. Simplify. a + 76 * 26 * u / 3080 = 112 * 77 / 3080 + 31 * 26 / 3080. Simplify. a + 76 * 26 * u / 3080 = 112 * 77 / 3080 + 31 * 26 / 3080. Simplify. a + 76 * 26 * u / 3080 = 112 * 77 / 3080 + 31 * 26 / 3080. Simplify. a + 76 * 26 * u / 3080 = 112 * 77 / 3080 + 31 * 26 / 3080. Simplify. a + 76 * 26 * u / 3080 = 112 * 77 / 3080 + 31 * 26 / 3080. Simplify. a + 76 *
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. From the first equation, we can solve for n: n = (143 - 18b)/54. Substituting this expression for n into the second equation, we get: 87((143 - 18b)/54) - 93b = 48. Simplifying this equation, we get: (143 - 18b) - 108b = 48. Solving for b, we get: -126b = -95. b = 95/126. Substituting this value of b into the first equation, we get: 54n + 18(95/126) = 143. Simplifying this equation, we get: 54n = 143 - 18(95/126). Solving for n, we get: n = (143 - 18(95/126))/54. Simplifying this expression, we get: n = 1. ### Answer: b = 95/126 and n = 1.
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)?
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. First, we can solve for e in the first equation: e = (103 - 7 * p) / 53 Then, we can substitute this value for e into the second equation: 69 * (103 - 7 * p) / 53 - 88 * p = 6 Simplifying this equation, we get: -1001 * p + 7017 = 0 Solving for p, we get: p = 7017 / 1001 Now, we can substitute this value for p into the first equation to solve for e: e = (103 - 7 * (7017 / 1001)) / 53 Simplifying this equation, we get: e = 103 / 53 Therefore, the costs of electricity (e) and petroleum (p) are: e = 103 / 53 p = 7017 / 1001 ### Answer: e = 103 / 53, p = 7017 / 1001
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations using the elimination method. Multiply the first equation by 24 and the second equation by 18 to get: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Multiply the first equation by 24 and the second equation by 18 to get: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Add the two equations to eliminate the variable p: First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24
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.
DeepSeek Math 7B Base:
Reasoning: 59c-34w=84 11c+42w=98 Multiply the first equation by 11 and the second equation by 59. 649c-374w=924 649c+2418w=5722 Subtract the first equation from the second equation. -374w-2418w=924-5722 -2792w=-4798 Divide both sides by -2792. w=1.72 Substitute w=1.72 into the first equation. 59c-34(1.72)=84 59c-58.48=84 Add 58.48 to both sides. 59c=142.48 Divide both sides by 59. c=2.41 ### Answer: c=2.41, w=1.72
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. First, we can solve the first equation for f: 45 * f + 42 * z = 101 45 * f = 101 - 42 * z f = (101 - 42 * z) / 45 Now, we can substitute this value of f into the second equation: 60 * z - 42 * f = 13 60 * z - 42 * ((101 - 42 * z) / 45) = 13 60 * z - (42 * (101 - 42 * z)) / 45 = 13 60 * z - (42 * 101 - 42 * 42 * z) / 45 = 13 60 * z - (4292 - 1764 * z) / 45 = 13 60 * z - 4292 / 45 + 1764 * z / 45 = 13 (60 * 45 * z - 4292 + 1764 * z) / 45 = 13 (2700 * z - 4292 + 1764 * z) / 45 = 13 (4464 * z - 4292) / 45 = 13 4464 * z - 4292 = 13 * 45 4464 * z = 13 * 45 + 4292 4464 * z = 567 + 4292 4464 * z = 4859 z = 4859 / 4464 z = 1.088 Now, we can substitute this value of z into the first equation: 45 * f + 42 * z = 101 45 * f + 42 * 1.088 = 101 45 * f + 45.70 = 101 45 * f = 101 - 45.70 45 * f = 55.30 f = 55.30 / 45 f = 1.23 Therefore, the solution to the system of equations is f = 1.23 and z = 1.088. ### Answer: f = 1.23 and z = 1.088
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.
DeepSeek Math 7B Base:
Reasoning: We can solve the system of equations by using the substitution method. 26 * p - 21 * u = 6 15 * p + 58 * u = 83 We can solve the first equation for p: 26 * p - 21 * u = 6 26 * p = 6 + 21 * u p = (6 + 21 * u) / 26 We can substitute this value of p into the second equation: 15 * p + 58 * u = 83 15 * (6 + 21 * u) / 26 + 58 * u = 83 We can solve this equation for u: 15 * (6 + 21 * u) / 26 + 58 * u = 83 15 * (6 + 21 * u) + 58 * u * 26 = 83 * 26 15 * 6 + 15 * 21 * u + 58 * u * 26 = 83 * 26 90 + 15 * 21 * u + 58 * u * 26 = 83 * 26 15 * 21 * u + 58 * u * 26 = 83 * 26 - 90 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 * u + 58 * u * 26 = 2158 15 * 21 *
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
DeepSeek Math 7B Base:
Reasoning: 1) 92 * n - 38 * s = 62 2) 59 * n + 8 * s = 75 Multiply equation 1) by 8 and equation 2) by 38. 1) 736 * n - 304 * s = 496 2) 2242 * n + 304 * s = 2850 Add the two equations together. 2978 * n = 3346 Divide both sides by 2978. n = 1.12310559006433 Substitute n = 1.12310559006433 into equation 1) and solve for s. 92 * 1.12310559006433 - 38 * s = 62 103.325633086001 - 38 * s = 62 Subtract 103.325633086001 from both sides. -38 * s = -41.325633086001 Divide both sides by -38. s = 1.08751665994739 ### Answer: n = 1.12310559006433, s = 1.08751665994739
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.
DeepSeek Math 7B Base:
Reasoning: 87 * z - 35 * e = 63 81 * z + 58 * e = 154 Multiply the first equation by 58 and the second equation by 35. 4926 * z - 1990 * e = 3582 2835 * z + 2030 * e = 5390 Subtract the second equation from the first equation. 2091 * z - 3920 * e = -1808 Divide both sides by 2091. z = -1808/2091 Substitute the value of z into the first equation. 87 * (-1808/2091) - 35 * e = 63 Multiply both sides by 2091. -157296 - 35 * 2091 * e = 131103 Add 157296 to both sides. -35 * 2091 * e = 282309 Divide both sides by -35 * 2091. e = -282309/(-35 * 2091) Simplify the right-hand side. e = 107/70 ### Answer: e = 107/70, z = -1808/2091
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.
DeepSeek Math 7B Base:
Reasoning: (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18. Multiply the first equation by 36 and the second equation by 44. (11 * t) * 36 + (44 * h) * 36 = 110 * 36 (98 * t) * 44 - (36 * h) * 44 = 18 * 44. Simplify. (11 * t) * 36 + (44 * h) * 36 = 110 * 36 (98 * t) * 44 - (36 * h) * 44 = 18 * 44. (11 * 36) * t + (44 * 36) * h = 110 * 36 (98 * 44) * t - (36 * 44) * h = 18 * 44. 396 * t + 1584 * h = 3960 4312 * t - 1584 * h = 792. Add the two equations. 396 * t + 1584 * h = 3960 4312 * t - 1584 * h = 792. (396 * t) + (1584 * h) + (4312 * t) - (1584 * h) = 3960 + 792. (396 * t) + (4312 * t) + (1584 * h) - (1584 * h) = 3960 + 792. (396 + 4312) * t + (1584 - 1584) * h = 3960 + 792. (396 + 4312) * t + (1584 - 1584) * h = 3960 + 792. 4708 * t + (1584 - 1584) * h = 3960 + 792. 4708 * t + (1584 - 1584) * h = 3960 + 792. 4708 * t + 0 * h = 3960 + 792. 4708 * t + 0 * h = 3960 + 792. 4708 * t + 0 = 3960 + 792. 4708 * t + 0 = 3960 + 792. 4708 * t = 3960 + 792. 4708 * t = 3960 + 792. 4708 * t = 4752. 4708 * t = 4752. t = 4752 / 4708. t = 4752 / 4708. t = 1.01008547008547. t = 1.01008547008547. 4708 * t = 4752. 4708 * t = 4752. 4708 * 1.01008547008547 = 4752. 4708 * 1.01008547008547 = 4752. 4752 = 4752. 4752 = 4752. 4708 * t = 4752. 4708 * t = 4752. 4708 * 1.010
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.
DeepSeek Math 7B Base:
Reasoning: 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o = 55 41o + 18b = 85 69b - 50o
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 6 * q + 5 * p = 177 6 * q = 177 - 5 * p q = (177 - 5 * p) / 6 67 * q - 80 * p = 65 67 * ((177 - 5 * p) / 6) - 80 * p = 65 (67 * (177 - 5 * p)) / 6 - 80 * p = 65 (67 * 177 - 67 * 5 * p) / 6 - 80 * p = 65 (11859 - 67 * 5 * p) / 6 - 80 * p = 65 (11859 - 67 * 5 * p) / 6 = 65 + 80 * p 11859 - 67 * 5 * p = 6 * (65 + 80 * p) 11859 - 67 * 5 * p = 390 + 6 * 80 * p 11859 - 67 * 5 * p = 390 + 480 * p 11859 - 390 = 480 * p + 67 * 5 * p 11469 = 480 * p + 67 * 5 * p 11469 = 480 * p + 335 * p 11469 = 815 * p p = 11469 / 815 p = 14.072 6 * q + 5 * p = 177 6 * q + 5 * 14.072 = 177 6 * q + 70.36 = 177 6 * q = 177 - 70.36 6 * q = 106.64 q = 106.64 / 6 q = 17.773 ### Answer: p = 14.072, q = 17.773
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 10 * k + 48 * f = 161 33 * k - 41 * f = 31 We can solve the first equation for k: k = (161 - 48 * f) / 10 We can then substitute this value of k into the second equation: 33 * ((161 - 48 * f) / 10) - 41 * f = 31 We can then solve for f: 33 * ((161 - 48 * f) / 10) - 41 * f = 31 (33 * (161 - 48 * f) - 410 * f) / 10 = 31 33 * (161 - 48 * f) - 410 * f = 310 5313 - 1584 * f - 410 * f = 310 -1994 * f = -5003 f = 2.51 We can then substitute this value of f into the first equation to solve for k: 10 * k + 48 * 2.51 = 161 10 * k + 120.48 = 161 10 * k = 40.52 k = 4.05 ### Answer: k = 4.05, f = 2.51
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
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. First, we can solve the first equation for n: n = 58 * l - 31 Then, we can substitute this expression for n into the second equation: 103 = (58 * l - 31) + 73 * l Simplifying this equation, we get: 103 = 131 * l - 31 Adding 31 to both sides of the equation, we get: 134 = 131 * l Dividing both sides of the equation by 131, we get: l = 134/131 Now, we can substitute this value for l into the first equation: 31 = 58 * (134/131) - n Simplifying this equation, we get: 31 = 58/131 - n Subtracting 58/131 from both sides of the equation, we get: n = 31 - 58/131 Simplifying this expression, we get: n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 31 * 131/131 - 58/131 n = 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
DeepSeek Math 7B Base:
Reasoning: 29y - 28j = 39 25y + 37j = 116 Multiply the first equation by 37 and the second equation by 28. 1073y - 1036j = 1443 700y + 1036j = 3248 Add the two equations. 1773y = 4691 Divide both sides by 1773. y = 2.64 Substitute y = 2.64 into the first equation. 29(2.64) - 28j = 39 Solve for j. j = 0.21 ### Answer: y = 2.64, j = 0.21
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.
DeepSeek Math 7B Base:
Reasoning: 93u - 85a = 74 96u + 17a = 186 Multiply the first equation by 17 and the second equation by 85. 1581u - 1445a = 1258 8160u + 1445a = 15810 Add the two equations together. 9741u = 17068 Divide both sides by 9741. u = 17068/9741 Substitute u = 17068/9741 into the first equation. 93(17068/9741) - 85a = 74 Multiply both sides by 9741. 93(17068) - 85a(9741) = 74(9741) Simplify. 1589946 - 85a(9741) = 728014 Subtract 1589946 from both sides. -85a(9741) = -861932 Divide both sides by -85(9741). a = 861932/85(9741) Simplify. a = 104/85 ### Answer: u = 17068/9741, a = 104/85
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
DeepSeek Math 7B Base:
Reasoning: 97 * u - 61 * g = 15 85 * u + 23 * g = 186 Multiply the first equation by 23 and the second equation by 61: 2231 * u - 1403 * g = 345 5185 * u + 1403 * g = 11346 Add the two equations: 7416 * u = 11691 u = 11691 / 7416 = <<11691/7416=1.58>>1.58 Substitute u = 1.58 into the first equation: 97 * 1.58 - 61 * g = 15 151.06 - 61 * g = 15 61 * g = 151.06 - 15 = 136.06 g = 136.06 / 61 = <<136.06/61=2.23>>2.23 ### Answer: u = 1.58, g = 2.23
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.
DeepSeek Math 7B Base:
Reasoning: The first equation is (17 * r) + (67 * b) = 103. The second equation is (85 * r) + (67 * b) = 187. We can solve for r by subtracting the first equation from the second equation. (85 * r) + (67 * b) = 187 - (17 * r) + (67 * b) = 103 (68 * r) = 84 r = 84/68 = <<84/68=1.2307692307692308>>1.2307692307692308 We can then substitute r = 1.2307692307692308 into the first equation to solve for b. (17 * 1.2307692307692308) + (67 * b) = 103 (20.923076923076923) + (67 * b) = 103 (67 * b) = 103 - 20.923076923076923 (67 * b) = 82.07692307692308 b = 82.07692307692308/67 = <<82.07692307692308/67=1.2250286740331476>>1.2250286740331476 ### Answer: r = 1.2307692307692308, b = 1.2250286740331476
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.
DeepSeek Math 7B Base:
Reasoning: 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126. Multiply the first equation by 30 and the second equation by 54 to get: 1. (2550 * n) - (1620 * t) = 1230 2. (2052 * t) + (1620 * n) = 6804. Subtract the first equation from the second equation to get: (2052 * t) - (2550 * n) = 5574. Divide both sides of the equation by 12 to get: (171 * t) - (212.5 * n) = 464.5. Multiply the first equation by 54 and the second equation by 5 to get: 1. (4620 * n) - (2916 * t) = 2148 2. (1020 * t) + (1500 * n) = 6300. Subtract the first equation from the second equation to get: (1020 * t) - (4620 * n) = 4152. Divide both sides of the equation by 10 to get: (102 * t) - (462 * n) = 415.2. Add the two equations to get: (342 * t) - (425 * n) = 880.2. Divide both sides of the equation by 342 to get: (t) - (1.24 * n) = 2.57. Multiply both sides of the equation by 1.24 to get: (t) - (1.51 * n) = 3.19. Add the two equations to get: (0.27 * n) = 0.62. Divide both sides of the equation by 0.27 to get: (n) = 2.3. Substitute the value of n into the first equation to get: (85 * 2.3) - (54 * t) = 41. Simplify the equation to get: (195.5) - (54 * t) = 41. Subtract 195.5 from both sides of the equation to get: (-54 * t) = -154.5. Divide both sides of the equation by -54 to get: (t) = 2.87. ### Answer: t = 2.87, n = 2.3
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.
DeepSeek Math 7B Base:
Reasoning: 1) 75u - 69q = 5 2) 48u + 25q = 140 Multiply the first equation by 25 and the second equation by 69. 1) 1875u - 1725q = 125 2) 3264u + 1725q = 9660 Add the two equations together. 1875u - 1725q + 3264u + 1725q = 125 + 9660 5139u = 9785 u = 9785/5139 u = <<9785/5139=1.9030000000000001>>1.903 Substitute the value of u into the first equation. 75(1.903) - 69q = 5 142.725 - 69q = 5 -69q = 5 - 142.725 -69q = -137.725 q = -137.725/-69 q = <<-137.725/-69=2.0000000000000004>>2.000 ### Answer: u = 1.903, q = 2.000
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. We can solve for v in the first equation: v = (149 - 17x) / 20. We can then substitute this value of v into the second equation: 24x - 49((149 - 17x) / 20) = 22. Simplifying this equation, we get: 108x - 3421 = 440. Solving for x, we get: x = 42. Substituting this value of x into the first equation, we get: 20v + 17(42) = 149. Solving for v, we get: v = -1. ### Answer: v = -1 and x = 42.
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 39 * t + 41 * g = 147 94 * t - 91 * g = 42. We can solve the first equation for t: 39 * t + 41 * g = 147 39 * t = 147 - 41 * g t = (147 - 41 * g) / 39 We can then substitute this value for t into the second equation: 94 * t - 91 * g = 42. 94 * ((147 - 41 * g) / 39) - 91 * g = 42. We can then solve for g: 94 * ((147 - 41 * g) / 39) - 91 * g = 42. (94 * (147 - 41 * g) - 91 * 39 * g) / 39 = 42. 94 * (147 - 41 * g) - 91 * 39 * g = 42 * 39 13878 - 3834 * g - 3561 * g = 1598 13878 - 7395 * g = 1598 7395 * g = 13878 - 1598 7395 * g = 12280 g = 12280 / 7395 g = 1.66 We can then substitute this value for g into the first equation to solve for t: 39 * t + 41 * g = 147 39 * t + 41 * 1.66 = 147 39 * t + 67.86 = 147 39 * t = 147 - 67.86 39 * t = 79.14 t = 79.14 / 39 t = 2.03 ### Answer: t = 2.03, g = 1.66
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the elimination method. Multiply the first equation by 48 and the second equation by 55 to get 312c + 2940o = 5376 and 3025c - 2640o = 1980. Subtracting the second equation from the first equation gives 2903c = 3396, so c = 3396/2903. Substituting this value of c into the first equation gives 55(3396/2903) - 48o = 36, so 48o = 55(3396/2903) - 36 = 112(55/2903) - 36 = 112(55/2903) - 36(2903/2903) = (112*55 - 36*2903)/2903 = 112*55/2903 - 36*2903/2903 = 112*55/2903 - 36 = 6272/2903 - 36 = 6272/2903 - 36(2903/2903) = (6272 - 36*2903)/2903 = -8500/2903. Therefore, c = 3396/2903 and o = -8500/2903. ### Answer: c = 3396/2903 and o = -8500/2903
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the elimination method. Multiply the first equation by 71 and the second equation by 8 to get: 568w + 4772u = 12070, 568w - 752u = 64. Subtract the second equation from the first equation to get: 5544u = 11426. Divide both sides by 5544 to get: u = 2.06. Substitute u = 2.06 into the first equation to get: 8w + 68(2.06) = 170. Simplify to get: 8w + 139.28 = 170. Subtract 139.28 from both sides to get: 8w = 30.72. Divide both sides by 8 to get: w = 3.84. ### Answer: u = 2.06, w = 3.84
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
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 68*r + 8*f = 92 97*f + 38*r = 182 We can solve the first equation for f: 8*f = 92 - 68*r f = (92 - 68*r)/8 We can then substitute this expression for f into the second equation: 97*((92 - 68*r)/8) + 38*r = 182 We can then solve for r: 97*(92 - 68*r) + 38*8*r = 182*8 9124 - 6572*r + 224*r = 1456 -6348*r = -7568 r = 1.19 We can then substitute this value for r into the first equation to solve for f: 68*1.19 + 8*f = 92 79.72 + 8*f = 92 8*f = 12.28 f = 1.53 ### Answer: r = 1.19, f = 1.53
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).
DeepSeek Math 7B Base:
Reasoning: We have two equations: 67d - 37r = 50 39r - 21d = 16 We can solve this system of equations using the substitution method. From the first equation, we can isolate d: 67d - 37r = 50 67d = 50 + 37r d = (50 + 37r) / 67 Now, we can substitute this expression for d in the second equation: 39r - 21d = 16 39r - 21((50 + 37r) / 67) = 16 Simplifying this equation, we get: 39r - (1050 + 777r) / 67 = 16 (2583r - 1050) / 67 = 16 2583r - 1050 = 1072 2583r = 2122 r = 2122 / 2583 Now, we can substitute this value of r in the expression for d: d = (50 + 37r) / 67 d = (50 + 37(2122 / 2583)) / 67 d = (50 + 78514 / 2583) / 67 d = (12914 / 2583) / 67 d = 12914 / (2583 * 67) d = 12914 / 173049 d = 0.0747 Therefore, the values of d and r are: d = 0.0747 r = 2122 / 2583 ### Answer: d = 0.0747 r = 2122 / 2583
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. First, we can solve the first equation for x: 163 = 50x + a 50x = 163 - a x = (163 - a) / 50 Next, we can substitute this value of x into the second equation: 24 = 98 * (163 - a) / 50 - 84a 24 = (16054 - 98a) / 50 - 84a 24 = 321.08 - 1.96a - 84a 24 = 321.08 - 85.96a 85.96a = 321.08 - 24 85.96a = 297.08 a = 297.08 / 85.96 a = 3.45 Now that we have the value of a, we can substitute it into the first equation to find the value of x: 163 = 50x + 3.45 50x = 163 - 3.45 50x = 159.55 x = 159.55 / 50 x = 3.19 Therefore, the values of x and a are x = 3.19 and a = 3.45. ### Answer: x = 3.19, a = 3.45
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 67 * p + 18 * b = 110 82 * b - 44 * p = 58. We can solve the first equation for p: 67 * p + 18 * b = 110 67 * p = 110 - 18 * b p = (110 - 18 * b) / 67 We can substitute this expression for p into the second equation: 82 * b - 44 * p = 58. 82 * b - 44 * ((110 - 18 * b) / 67) = 58. We can solve this equation for b: 82 * b - 44 * ((110 - 18 * b) / 67) = 58. 82 * b - (44 * (110 - 18 * b)) / 67 = 58. 82 * b - (44 * 110 - 44 * 18 * b) / 67 = 58. 82 * b - (4840 - 792 * b) / 67 = 58. 82 * b - 4840 / 67 + 792 * b / 67 = 58. 82 * b + 792 * b / 67 - 4840 / 67 = 58. (82 * 67 * b + 792 * b) / 67 - 4840 / 67 = 58. (5554 * b + 792 * b) / 67 - 4840 / 67 = 58. (6346 * b) / 67 - 4840 / 67 = 58. 6346 * b / 67 - 4840 / 67 = 58. 6346 * b - 4840 = 58 * 67. 6346 * b - 4840 = 3886. 6346 * b = 3886 + 4840. 6346 * b = 8726. b = 8726 / 6346. b = 1.380952380952381. We can substitute this value for b into the first equation: 67 * p + 18 * b = 110. 67 * p + 18 * 1.380952380952381 = 110. 67 * p + 24.857142857142855 = 110. 67 * p = 110 - 24.857142857142855. 67 * p = 85.14285714285714. p = 85.14285714285714 / 67. p = 1.2708381270838127. ### Answer: p = 1.2708381270838127, b = 1.380952380952381.
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.
DeepSeek Math 7B Base:
Reasoning: 63c-36e=27 and 8c+32e=69. Multiply the first equation by 4 to get 252c-144e=108. Multiply the second equation by 9 to get 72c+288e=621. Subtract the first equation from the second equation to get 174c+432e=513. Divide both sides of the equation by 174 to get c+2.4242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242
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
DeepSeek Math 7B Base:
Reasoning: 26 * x + 29 * p = 107 61 * x - 51 * p = 4 Multiply the first equation by 51 and the second equation by 29: 1326 * x + 1489 * p = 5517 1769 * x - 1489 * p = 116 Add the two equations: 3095 * x = 5633 Divide both sides by 3095: x = 1.818 Substitute the value of x into the first equation: 26 * 1.818 + 29 * p = 107 29 * p = 107 - 47.268 29 * p = 59.732 Divide both sides by 29: p = 2.06 ### Answer: x = 1.818, p = 2.06
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. First, we can solve for l in the first equation: ((29 * l) + (17 * g)) = 68 (29 * l) = 68 - (17 * g) l = (68 - (17 * g)) / 29 Now, we can substitute this value for l into the second equation: ((31 * g) - (10 * l)) = 17 ((31 * g) - (10 * ((68 - (17 * g)) / 29))) = 17 (31 * g) - ((680 - (170 * g)) / 29) = 17 (31 * g) - (680 / 29) + ((170 * g) / 29) = 17 (31 * g) + ((170 * g) / 29) = 17 + (680 / 29) ((841 * g) / 29) = (17 + (680 / 29)) (841 * g) = (17 + (680 / 29)) * 29 g = ((17 + (680 / 29)) * 29) / 841 Now, we can substitute this value for g into the first equation: ((29 * l) + (17 * g)) = 68 ((29 * l) + (17 * ((17 + (680 / 29)) * 29) / 841)) = 68 (29 * l) + ((493 + (11560 / 29)) * 29) / 841 = 68 (29 * l) + (493 * 29) / 841 + ((11560 / 29) * 29) / 841 = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l) + (493 * 29) / 841 + (11560 / 841) = 68 (29 * l
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. First, we can solve for a in the first equation: a = (20 + 54*c) / 33 Then, we can substitute this value for a into the second equation: 24*((20 + 54*c) / 33) - 26*c = 29 Simplifying this equation, we get: (24*20 + 24*54*c - 26*33*c) / 33 = 29 Multiplying both sides by 33, we get: 24*20 + 24*54*c - 26*33*c = 33*29 Simplifying this equation, we get: 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*20 + 24*54*c - 26*33*c = 33*29 24*
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the elimination method. 71d + 9j = 132 43j - 84d = 91. Multiply the first equation by 84 and the second equation by 71 to get: 5844d + 756j = 11088 3037j - 5964d = 6441. Add the two equations to get: 5844d + 756j = 11088 3037j - 5964d = 6441. 8581j = 17529. Divide both sides by 8581 to get: j = 17529/8581. Substitute the value of j into the first equation to get: 71d + 9(17529/8581) = 132. Multiply both sides by 8581 to get: 57737d + 157761 = 11088. Subtract 157761 from both sides to get: 57737d = -46873. Divide both sides by 57737 to get: d = -46873/57737. ### Answer: d = -46873/57737, j = 17529/8581
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143 We can solve for o in the first equation: (81 * o) + (26 * n) = 163 81 * o = 163 - 26 * n o = (163 - 26 * n) / 81 We can then substitute this value of o into the second equation: (87 * n) + (23 * o) = 143 (87 * n) + (23 * (163 - 26 * n) / 81) = 143 We can then solve for n: (87 * n) + (23 * (163 - 26 * n) / 81) = 143 (87 * n) + (23 * 163 / 81) - (23 * 26 * n / 81) = 143 (87 * n) - (23 * 26 * n / 81) = 143 - (23 * 163 / 81) (87 * n - 23 * 26 * n / 81) / (87 - 23 * 26 / 81) = (143 - 23 * 163 / 81) / (87 - 23 * 26 / 81) n = (143 - 23 * 163 / 81) / (87 - 23 * 26 / 81) n = <<(143 - 23 * 163 / 81) / (87 - 23 * 26 / 81)>> We can then substitute this value of n into the first equation to solve for o: (81 * o) + (26 * n) = 163 (81 * o) + (26 * <<(143 - 23 * 163 / 81) / (87 - 23 * 26 / 81)>>) = 163 (81 * o) = 163 - (26 * <<(143 - 23 * 163 / 81) / (87 - 23 * 26 / 81)>>) o = (163 - (26 * <<(143 - 23 * 163 / 81) / (87 - 23 * 26 / 81)>>)) / 81 o = <<(163 - (26 * <<(143 - 23 * 163 / 81) / (87 - 23 * 26 / 81)>>)) / 81>> ### Answer: o = <<(163 - (26 * <<(143 - 23 * 163 / 81) / (87 - 23 * 26 / 81)>>)) / 81>>, n = <<(143 - 23 * 163 / 81) / (87 - 23 * 26 / 81)>>
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 46 * s - 61 * w = 2 61 * s + 67 * w = 178. We can solve the first equation for s: 46 * s - 61 * w = 2 46 * s = 2 + 61 * w s = (2 + 61 * w) / 46 We can then substitute this expression for s into the second equation: 61 * s + 67 * w = 178. 61 * (2 + 61 * w) / 46 + 67 * w = 178. We can then solve for w: 61 * (2 + 61 * w) / 46 + 67 * w = 178. 61 * (2 + 61 * w) + 67 * w * 46 = 178 * 46 61 * 2 + 61 * 61 * w + 67 * w * 46 = 178 * 46 61 * 2 + 61 * 61 * w + 2982 * w = 178 * 46 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 * 2 + 61 * 61 * w + 2982 * w = 8068 61 *
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.
DeepSeek Math 7B Base:
Reasoning: 51*k - 8*i = 86 39*i + 8*k = 193. Multiply the first equation by 39 and the second equation by 51. 39*51*k - 39*8*i = 39*86 51*39*i + 51*8*k = 51*193. Simplify the equations. 1989*k - 312*i = 3354 1989*i + 408*k = 9783. Subtract the second equation from the first. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 1989*k - 312*i = 3354 -1989*i - 408*k = -9783. 19
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
DeepSeek Math 7B Base:
Reasoning: 26m + 17l = 146 93m + l = 126 Multiply the second equation by 17: 26m + 17l = 146 1581m + 17l = 2142 Subtract the first equation from the second: 1555m = 1996 Divide both sides by 1555: m = 1996/1555 Substitute the value of m into the second equation: 93(1996/1555) + l = 126 Simplify: l = 126 - 93(1996/1555) Simplify: l = 126 - 124.56 l = 1.44 ### Answer: m = 1996/1555, l = 1.44
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
DeepSeek Math 7B Base:
Reasoning: 1) (8 * f) + (39 * h) = 66 2) (29 * f) + (46 * h) = 119 Multiply equation 1) by 29 and equation 2) by 8. 1) (8 * f) + (39 * h) = 66 2) (29 * f) + (46 * h) = 119 1) (29 * 8) * f + (29 * 39) * h = 29 * 66 2) (8 * 29) * f + (8 * 46) * h = 8 * 119 1) (232) * f + (1131) * h = 1914 2) (232) * f + (368) * h = 952 Subtract equation 2) from equation 1). 1) (232) * f + (1131) * h = 1914 2) (232) * f + (368) * h = 952 1) (1131) * h = 962 2) (368) * h = 952 Divide equation 1) by 1131 and equation 2) by 368. 1) (1131) * h = 962 2) (368) * h = 952 1) h = 962/1131 2) h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952/368 h = 962/1131 h = 952
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 22 * b + 23 * k = 109 22 * b = 109 - 23 * k b = (109 - 23 * k) / 22 62 * k - 69 * b = 14 62 * k - 69 * ((109 - 23 * k) / 22) = 14 62 * k - (69 * (109 - 23 * k)) / 22 = 14 1364 * k - 69 * (109 - 23 * k) = 28 1364 * k - 7269 + 1587 * k = 28 2951 * k = 7297 k = 7297 / 2951 k = 2.472 b = (109 - 23 * 2.472) / 22 b = 2.028 ### Answer: k = 2.472, b = 2.028
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.
DeepSeek Math 7B Base:
Reasoning: 1. 84m - 55s = 1 2. 63m - 2s = 98. Multiply the first equation by 2 and the second equation by 55 to get: 1. 168m - 110s = 2 2. 3465m - 110s = 5390. Subtract the first equation from the second equation to get: 3449m = 5388. Divide both sides by 3449 to get: m = 5388/3449 = <<5388/3449=1.5625>>1.5625. Substitute m = 1.5625 into the first equation to get: 84(1.5625) - 55s = 1. Simplify to get: 129.75 - 55s = 1. Subtract 129.75 from both sides to get: -55s = -128.75. Divide both sides by -55 to get: s = 128.75/55 = <<128.75/55=2.34>>2.34. ### Answer: m = 1.5625, s = 2.34
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.
DeepSeek Math 7B Base:
Reasoning: 1. (6 * b) + (5 * k) = 105 2. (95 * k) - (51 * b) = 67. Multiply the first equation by 51 and the second equation by 6 to get: 1. (306 * b) + (255 * k) = 5355 2. (570 * k) - (306 * b) = 402. Add the two equations to get: (255 * k) + (570 * k) = 5355 + 402. Simplify to get: (825 * k) = 5757. Divide both sides by 825 to get: k = 7. Substitute k = 7 into the first equation to get: (6 * b) + (5 * 7) = 105. Simplify to get: (6 * b) + 35 = 105. Subtract 35 from both sides to get: (6 * b) = 70. Divide both sides by 6 to get: b = 11.666666666666666. ### Answer: b = 11.666666666666666, k = 7.
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 33d + 62u = 114 32u + 40d = 83 We can solve for d in the first equation: 33d + 62u = 114 33d = 114 - 62u d = (114 - 62u) / 33 We can substitute this value of d into the second equation: 32u + 40d = 83 32u + 40((114 - 62u) / 33) = 83 32u + (40/33)(114 - 62u) = 83 32u + (40/33)(114) - (40/33)(62u) = 83 32u + (4560/33) - (2480/33)u = 83 (32 - (2480/33))u + (4560/33) = 83 (-2136/33)u + (4560/33) = 83 (-2136/33)u = 83 - (4560/33) (-2136/33)u = (2751/33) u = (2751/33) / (-2136/33) u = (2751/33) * (-33/2136) u = -2751/2136 u = -917/712 We can substitute this value of u into the first equation: 33d + 62u = 114 33d + 62(-917/712) = 114 33d - (56434/712) = 114 33d = 114 + (56434/712) 33d = (8020/712) + (56434/712) 33d = (64454/712) d = (64454/712) / 33 d = (64454/712) * (1/33) d = 64454/23496 d = 32227/11748 Therefore, the values of d and u are d = 32227/11748 and u = -917/712. ### Answer: d = 32227/11748 and u = -917/712
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
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the elimination method. Multiply the first equation by 20 to get 100 * c + 560 * p = 2040. Multiply the second equation by 5 to get 100 * c - 335 * p = 65. Subtract the second equation from the first equation to get 895 * p = 1975. Divide both sides by 895 to get p = 2.1. Substitute p = 2.1 into the first equation to get 5 * c + 28 * 2.1 = 102. Simplify to get 5 * c + 58.8 = 102. Subtract 58.8 from both sides to get 5 * c = 43.2. Divide both sides by 5 to get c = 8.64. ### Answer: c = 8.64, p = 2.1
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. We can solve for r in the first equation: r = (147 - 12 * q) / 58. We can then substitute this value of r into the second equation: 97 * q - 76 * ((147 - 12 * q) / 58) = 76. We can then solve for q: q = 1. We can then substitute this value of q into the first equation: 58 * r + 12 * 1 = 147. We can then solve for r: r = 2. ### Answer: r = 2, q = 1
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.
DeepSeek Math 7B Base:
Reasoning: 47 * v - 3 * k = 10 73 * v + 2 * k = 128 Multiply the first equation by 2 and the second equation by 3: 94 * v - 6 * k = 20 219 * v + 6 * k = 384 Add the two equations: 313 * v = 384 + 20 = 404 v = 404/313 = <<404/313=1.2907664233576642335766423357664>>1.2907664233576642335766423357664 Substitute v = 1.2907664233576642335766423357664 into the first equation: 47 * 1.2907664233576642335766423357664 - 3 * k = 10 59.665993896709938967099389670994 - 3 * k = 10 -3 * k = 10 - 59.665993896709938967099389670994 = -49.665993896709938967099389670994 k = -49.665993896709938967099389670994/-3 = <<-49.665993896709938967099389670994/-3=16.555331298903312989033129890331>>16.555331298903312989033129890331 ### Answer: v = 1.2907664233576642335766423357664, k = 16.555331298903312989033129890331
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?
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations using the substitution method. First, we can solve for p in the first equation: p = (41q + 60) / 89 Then, we can substitute this value of p into the second equation: 27 * ((41q + 60) / 89) + 91q = 124 Simplifying this equation, we get: 1107q + 1620 = 10639 Solving for q, we get: q = 8 Now, we can substitute this value of q into the first equation to solve for p: p = (41 * 8 + 60) / 89 p = 4 Therefore, the values of p and q are 4 and 8, respectively. ### Answer: p = 4, q = 8
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
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations using the substitution method. First, we can solve for u in the first equation: (88 * u) - (96 * d) = 12 88u - 96d = 12 88u = 12 + 96d u = (12 + 96d) / 88 Now, we can substitute this value of u into the second equation: (27 * u) + (36 * d) = 71 27 * ((12 + 96d) / 88) + 36d = 71 (27 * (12 + 96d)) / 88 + 36d = 71 (324 + 2592d) / 88 + 36d = 71 (324 + 2592d) / 88 = 71 - 36d 324 + 2592d = 88 * (71 - 36d) 324 + 2592d = 6248 - 3168d 5760d = 6248 - 324 5760d = 5924 d = 5924 / 5760 d = 1.028125 Now, we can substitute this value of d into the first equation to find the value of u: u = (12 + 96d) / 88 u = (12 + 96 * 1.028125) / 88 u = (12 + 99.6) / 88 u = 111.6 / 88 u = 1.265625 Therefore, the values of u and d that make these equations true are u = 1.265625 and d = 1.028125. ### Answer: u = 1.265625 and d = 1.028125
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.
DeepSeek Math 7B Base:
Reasoning: 20 * n - 18 * f = 9 3 * n - 2 * f = 70 Multiply the second equation by 6: 18 * n - 12 * f = 420 Subtract the first equation from the second equation: 18 * n - 12 * f = 420 - 20 * n - 18 * f = 9 - 2 * n = 411 Divide both sides by 2: n = 205.5 Substitute n = 205.5 into the first equation: 20 * 205.5 - 18 * f = 9 4110 - 18 * f = 9 Subtract 4110 from both sides: -18 * f = -4101 Divide both sides by -18: f = 227.83333333333333 ### Answer: f = 227.83333333333333, n = 205.5
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. From the first equation, we can solve for l: 7 * l + 97 * j = 133 7 * l = 133 - 97 * j l = (133 - 97 * j) / 7 Substituting this expression for l into the second equation, we get: 22 * j + 37 * ((133 - 97 * j) / 7) = 76 Simplifying this equation, we get: 22 * j + 37 * (133 - 97 * j) / 7 = 76 Multiplying both sides by 7, we get: 154 * j + 37 * (133 - 97 * j) = 532 Expanding the parentheses, we get: 154 * j + 4921 - 3649 * j = 532 Simplifying this equation, we get: -2105 * j = -4389 Solving for j, we get: j = 4389 / 2105 j = 2.086 Substituting this value of j into the expression for l, we get: l = (133 - 97 * 2.086) / 7 l = -0.086 ### Answer: j = 2.086, l = -0.086
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.
DeepSeek Math 7B Base:
The first step is to solve for d in the first equation. 21d - 46f = 53 21d = 53 + 46f d = (53 + 46f)/21 Now, we can substitute this value of d into the second equation: 8d + 84f = 133 8((53 + 46f)/21) + 84f = 133 (424 + 368f)/21 + 84f = 133 424 + 368f + 1764f = 2793 2132f = 2369 f = 2369/2132 Now, we can substitute this value of f into the first equation to find the value of d: 21d - 46f = 53 21d - 46(2369/2132) = 53 21d - 46(1.158) = 53 21d - 52.368 = 53 21d = 105.368 d = 5.017 So, the values of d and f are d = 5.017 and f = 2369/2132. ### Answer: d = 5.017, f = 2369/2132
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.
DeepSeek Math 7B Base:
The first step is to solve for one of the variables in one of the equations. 74u + 11w = 116 11w = 116 - 74u w = (116 - 74u)/11
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 76 * f - 42 * j = 96 47 * j + 34 * f = 136 We can solve the first equation for f: 76 * f - 42 * j = 96 76 * f = 96 + 42 * j f = (96 + 42 * j) / 76 We can then substitute this value of f into the second equation: 47 * j + 34 * f = 136 47 * j + 34 * ((96 + 42 * j) / 76) = 136 47 * j + 34 * (96 + 42 * j) / 76 = 136 47 * j + (34 * 96 + 34 * 42 * j) / 76 = 136 47 * j + (3312 + 1428 * j) / 76 = 136 Multiplying both sides by 76: 47 * j * 76 + (3312 + 1428 * j) = 136 * 76 3572 * j + 3312 + 1428 * j = 10336 4992 * j + 3312 = 10336 4992 * j = 10336 - 3312 4992 * j = 7024 j = 7024 / 4992 j = 1.40625 We can then substitute this value of j into the first equation to find the value of f: 76 * f - 42 * j = 96 76 * f - 42 * 1.40625 = 96 76 * f - 59.0625 = 96 76 * f = 96 + 59.0625 76 * f = 155.0625 f = 155.0625 / 76 f = 2.040333333333333 ### Answer: f = 2.040333333333333, j = 1.40625
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the elimination method. Multiply the first equation by 69 and the second equation by 32, and then add the two equations together. 68u + 32e = 174 63e - 69u = 1 69(68u + 32e) + 32(63e - 69u) = 69(174) + 32(1) 4692u + 2112e + 2016e - 2208u = 11706 + 32 2484u + 4128e = 11738 Divide both sides by 2484. u + 1.66e = 4.72 Multiply both sides by 1.66. 1.66u + 2.7556e = 7.8052 Multiply both sides by 100. 166u + 275.56e = 780.52 Multiply both sides by 100. 166u + 275.56e = 780.52 Subtract 275.56e from both sides. 166u = 780.52 - 275.56e Divide both sides by 166. u = 4.72 - 1.66e Substitute 4.72 - 1.66e for u in the first equation. 68(4.72 - 1.66e) + 32e = 174 319.36 - 112.88e + 32e = 174 Subtract 319.36 from both sides. -112.88e + 32e = 174 - 319.36 -80.88e = -145.36 Divide both sides by -80.88. e = 1.797 Substitute 1.797 for e in the first equation. 68u + 32(1.797) = 174 68u + 57.504 = 174 Subtract 57.504 from both sides. 68u = 174 - 57.504 68u = 116.496 Divide both sides by 68. u = 1.714 ### Answer: u = 1.714, e = 1.797
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of linear equations by using the substitution method. From the first equation, we can solve for p in terms of n: p = (129 - 4n) / 57 Substituting this expression for p into the second equation, we get: 24((129 - 4n) / 57) + 39n = 154 Simplifying this equation, we get: (129 - 4n) / 2.333333333333333 + 39n = 154 Multiplying both sides by 2.333333333333333, we get: 129 - 4n + 89.99999999999999n = 358.6666666666667 Simplifying this equation, we get: 49.99999999999999n = 229.6666666666667 Dividing both sides by 49.99999999999999, we get: n = 4.600000000000001 Substituting this value for n into the expression for p, we get: p = (129 - 4(4.600000000000001)) / 57 Simplifying this expression, we get: p = 2.000000000000001 ### Answer: p = 2.000000000000001 and n = 4.600000000000001
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 66 * z - 44 * y = 32 60 * y + 14 * z = 116. Solving the first equation for y, we get: y = (66 * z - 32) / 44 Substituting this expression for y into the second equation, we get: 60 * ((66 * z - 32) / 44) + 14 * z = 116 Simplifying, we get: 15 * (66 * z - 32) + 14 * z = 116 Expanding the left-hand side, we get: 990 * z - 480 + 14 * z = 116 Combining like terms, we get: 1004 * z = 604 Dividing both sides by 1004, we get: z = 604/1004 Simplifying, we get: z = 151/251 Substituting this value of z into the first equation, we get: 66 * (151/251) - 44 * y = 32 Simplifying, we get: -44 * y = 32 - 9966/251 Simplifying, we get: -44 * y = -10034/251 Dividing both sides by -44, we get: y = 10034/11044 Simplifying, we get: y = 5017/5522 ### Answer: y = 5017/5522, z = 151/251
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. From the first equation, we can solve for t: t = (58 * h + 45) / 83 Substituting this expression for t into the second equation, we get: 69 * h + 11 * (58 * h + 45) / 83 = 124 Simplifying this equation, we get: (69 * 83 * h + 11 * 58 * h + 11 * 45) / 83 = 124 Multiplying both sides by 83, we get: 69 * 83 * h + 11 * 58 * h + 11 * 45 = 124 * 83 Simplifying this equation, we get: 5817 * h + 638 * h + 495 = 10292 Combining like terms, we get: 6455 * h + 495 = 10292 Subtracting 495 from both sides, we get: 6455 * h = 9797 Dividing both sides by 6455, we get: h = 1.5176 Substituting this value of h into the expression for t, we get: t = (58 * 1.5176 + 45) / 83 Simplifying this expression, we get: t = 1.1035 ### Answer: t = 1.1035, h = 1.5176
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?
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the elimination method. Multiply the first equation by 12 and the second equation by 61 to get: ((12 * 79) * h) - ((12 * 61) * o) = (12 * 9) and ((61 * 16) * h) - ((61 * 12) * o) = (61 * 9) Simplify: ((12 * 79) * h) - ((12 * 61) * o) = (12 * 9) and ((61 * 16) * h) - ((61 * 12) * o) = (61 * 9) ((948) * h) - ((732) * o) = (108) and ((976) * h) - ((732) * o) = (549) Subtract the second equation from the first equation: ((948) * h) - ((732) * o) = (108) and ((976) * h) - ((732) * o) = (549) ((948) * h) - ((976) * h) = (108) - (549) ((948) - (976)) * h = (108) - (549) (-28) * h = (-441) h = (-441) / (-28) h = (15.75) Substitute h = (15.75) into the first equation: ((79) * h) - (61 * o) = 9 ((79) * (15.75)) - (61 * o) = 9 (1236.75) - (61 * o) = 9 (1236.75) - 9 = (61 * o) (1227.75) = (61 * o) o = (1227.75) / (61) o = (20.127) ### Answer: o = (20.127) and h = (15.75)
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
DeepSeek Math 7B Base:
Reasoning: 4 * y + 56 * s = 139 65 * y - 90 * s = 16 Multiply the first equation by 15 and the second equation by 4 to get: 60 * y + 840 * s = 2085 260 * y - 360 * s = 64 Add the two equations to get: 320 * y = 2149 Divide both sides by 320 to get: y = 2149/320 Substitute the value of y into the first equation to get: 4 * (2149/320) + 56 * s = 139 Simplify to get: 56 * s = 139 - 4 * (2149/320) Simplify further to get: 56 * s = 139 - 2149/80 Multiply both sides by 1/56 to get: s = (139 - 2149/80) / 56 Simplify to get: s = (139 * 80 - 2149) / (56 * 80) Simplify further to get: s = (11120 - 2149) / 4480 Simplify further to get: s = 8971/4480 ### Answer: s = 8971/4480, y = 2149/320
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.
DeepSeek Math 7B Base:
Reasoning: 42 * d - 4 * z = 75 40 * d + 45 * z = 162 Multiply the first equation by 45 and the second equation by 4 to get: 42 * 45 * d - 4 * 45 * z = 75 * 45 40 * 4 * d + 45 * 4 * z = 162 * 4 Simplify: 1890 * d - 180 * z = 3375 160 * d + 180 * z = 648 Add the two equations to get: 1890 * d + 160 * d = 3375 + 648 Simplify: 2050 * d = 4023 Divide both sides by 2050 to get: d = 4023/2050 Substitute the value of d into the first equation to get: 42 * 4023/2050 - 4 * z = 75 Simplify: 169026/2050 - 4 * z = 75 Multiply both sides by 2050 to get: 169026 - 4 * 2050 * z = 75 * 2050 Simplify: 169026 - 8200 * z = 153750 Subtract 169026 from both sides to get: -8200 * z = -15276 Divide both sides by -8200 to get: z = 15276/8200 Simplify: z = 3819/2050 ### Answer: d = 4023/2050, z = 3819/2050
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.
DeepSeek Math 7B Base:
The first equation is: (42 * o) + (24 * a) = 142. The second equation is: (42 * a) + (6 * o) = 75. We can solve this system of equations using the substitution method. From the first equation, we can isolate o: (42 * o) + (24 * a) = 142 42 * o = 142 - 24 * a o = (142 - 24 * a) / 42 Now, we can substitute this expression for o in the second equation: (42 * a) + (6 * o) = 75 42 * a + 6 * (142 - 24 * a) / 42 = 75 42 * a + (142 - 24 * a) / 7 = 75 42 * a + 142 / 7 - 24 * a / 7 = 75 (42 * a - 24 * a) / 7 + 142 / 7 = 75 18 * a / 7 + 142 / 7 = 75 18 * a / 7 = 75 - 142 / 7 18 * a / 7 = (75 * 7 - 142) / 7 18 * a = (75 * 7 - 142) a = (75 * 7 - 142) / 18 Now, we can substitute this value of a in the expression for o: o = (142 - 24 * a) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 42 o = (142 - 24 * (75 * 7 - 142) / 18) / 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.
DeepSeek Math 7B Base:
Reasoning: 39*r - 2*p = 45 16*p - 84*r = 36 Multiply the first equation by 4: 156*r - 8*p = 180 Multiply the second equation by 3: 48*p - 252*r = 108 Add the two equations: 33*p = 288 p = 288/33 = <<288/33=8.727272727272727>>8.727272727272727 Substitute the value of p into the first equation: 39*r - 2*8.727272727272727 = 45 39*r = 45 + 17.454545454545455 = <<45+17.454545454545455=62.45454545454545>>62.45454545454545 r = 62.45454545454545/39 = <<62.45454545454545/39=1.6014014014014014>>1.6014014014014014 ### Answer: p = 8.727272727272727 and r = 1.6014014014014014
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
DeepSeek Math 7B Base:
Reasoning: 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58 Multiply the first equation by 4: 1. (92 * d) - (208 * w) = 28 2. (64 * w) - (8 * d) = 58 Add the two equations: (92 * d) - (208 * w) + (64 * w) - (8 * d) = 28 + 58 Simplify: (84 * d) - (144 * w) = 86 Divide both sides by 84: d - (1.7 * w) = 1.02 Add (1.7 * w) to both sides: d = 1.02 + (1.7 * w) Substitute this value of 'd' into the second equation: (64 * w) - (8 * (1.02 + (1.7 * w))) = 58 Simplify: (64 * w) - (8.16 + (13.6 * w)) = 58 Combine like terms: (50.4 * w) - 8.16 = 58 Add 8.16 to both sides: (50.4 * w) = 66.16 Divide both sides by 50.4: w = 1.31 Substitute this value of 'w' into the first equation: (23 * d) - (52 * 1.31) = 7 Simplify: (23 * d) - 68.12 = 7 Add 68.12 to both sides: (23 * d) = 75.12 Divide both sides by 23: d = 3.27 ### Answer: d = 3.27, w = 1.31
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19. We can solve for z in the first equation: z = (184 - 60n) / 71 We can then substitute this value of z into the second equation: (52 * ((184 - 60n) / 71)) - (47 * n) = 19. We can then solve for n: n = (19 - 52 * ((184 - 60n) / 71)) / -47 n = 1. We can then substitute this value of n into the first equation: (71 * z) + (60 * 1) = 184 We can then solve for z: z = (184 - 60) / 71 z = 2. ### Answer: n = 1, z = 2
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
DeepSeek Math 7B Base:
Reasoning: 70 * e + 90 * z = 189 99 * z - 84 * e = 20 Multiply the first equation by 84 and the second equation by 70 to get: 5880 * e + 7560 * z = 15624 6930 * z - 5880 * e = 1400 Add the two equations to get: 12450 * z = 17024 Divide both sides by 12450 to get: z = 17024/12450 Substitute the value of z into the first equation to get: 70 * e + 90 * (17024/12450) = 189 Simplify the equation to get: 70 * e + 123192/1245 = 189 Multiply both sides by 1245 to get: 8715 * e + 123192 = 237045 Subtract 123192 from both sides to get: 8715 * e = 113853 Divide both sides by 8715 to get: e = 113853/8715 ### Answer: e = 113853/8715, z = 17024/12450
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.
DeepSeek Math 7B Base:
Reasoning: We can solve this system of equations by using the substitution method. 1) 26o - 44f = 95 2) 87f + 11o = 169. From equation 2), we can solve for o: 87f + 11o = 169 11o = 169 - 87f o = (169 - 87f) / 11 Substituting this expression for o into equation 1), we get: 26((169 - 87f) / 11) - 44f = 95 (26(169 - 87f) - 44f * 11) / 11 = 95 26(169 - 87f) - 44f * 11 = 95 * 11 4394 - 2262f - 484f = 1045 -2262f - 484f = 1045 - 4394 -2746f = -3349 f = -3349 / -2746 f = 1.22 Substituting this value for f into the expression for o, we get: o = (169 - 87f) / 11 o = (169 - 87 * 1.22) / 11 o = (169 - 106.14) / 11 o = 62.86 / 11 o = 5.71 Therefore, the values of o and f that satisfy the system of equations are o = 5.71 and f = 1.22. ### Answer: o = 5.71, f = 1.22
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.
DeepSeek Math 7B Base:
Solving the system of equations: 40*z - 20*p = 51 6*z + 58*p = 165 Multiply the first equation by 3 and the second equation by 10: 120*z - 60*p = 153 60*z + 580*p = 1650 Subtract the second equation from the first: -680*p = -1497 Divide both sides by -680: p = 2.2 Substitute the value of p into the first equation: 40*z - 20*2.2 = 51 40*z - 44 = 51 Add 44 to both sides: 40*z = 95 Divide both sides by 40: z = 2.375 ### Answer: z = 2.375, p = 2.2
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.
DeepSeek Math 7B Base:
Reasoning: (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93 Multiply the second equation by 89: (71 * s) - (89 * f) = 5 (89 * 3 * f) + (89 * 10 * s) = 89 * 93 Add the two equations: (71 * s) - (89 * f) + (89 * 3 * f) + (89 * 10 * s) = 5 + 89 * 93 Simplify: (71 * s) + (89 * 3 * f) + (89 * 10 * s) = 5 + 89 * 93 (71 * s) + (89 * 3 * f) + (89 * 10 * s) = 8264 (71 * s) + (89 * 3 * f) + (89 * 10 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 * f) + (890 * s) = 8264 (71 * s) + (267 *
Expected answer: {f: 6553/1103, s: 8292/1103}
Correct? No