InternLM-Math Base 7B on 8.EE.C.8
Common Core Standard 8.EE.C.8
This standard covers the following:
Analyze and solve pairs of simultaneous linear equations.
Problem: Let's find the values of variables q and s by solving the following system of equations: 1. (40 * s) - (91 * q) = 37 2. (30 * s) + (12 * q) = 121
InternLM-Math Base 7B:
1. (30 * s) + (12 * q) = 121
Expected answer: {q: 373/321, s: 2291/642}
Correct? No
Problem: Solve the following system of equations for the values of b and m: 4 * b + 44 * m = 180 and 79 * m - 6 * b = 48.
InternLM-Math Base 7B:
Reasoning: 4 * b + 44 * m = 180 4 * b = 180 - 44 * m 4 * b = 36 * m 4 = 36 * m / b 4 = 36 * m / 4 1 = 9 * m / 1 1 = 9 * m 1/9 = m 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9 = 1/9 1/9
Expected answer: {b: 3027/145, m: 318/145}
Correct? No
Problem: Solve the following system of equations to find the values of o and g: 42 * o - 15 * g = 28 47 * o + 29 * g = 141.
InternLM-Math Base 7B:
Reasoning: 47*o + 29*g = 141 42*o - 15*g = 28 - 15*g = 28 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g = 14 - 42*o - 15*g =
Expected answer: {g: 4606/1923, o: 2927/1923}
Correct? No
Problem: Given the following system of equations, determine the values of v and o: The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50.
InternLM-Math Base 7B:
Reasoning: The first equation is: 12v-6o=21. The second equation is: 76v-45o=50. Solve the first equation for v: 12v-6o=21 12v=6o+21 v=1/2o+3/2 1/2o-3/2v=0 1/2o=3/2v 3o=6v 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3o-6v=0 3
Expected answer: {o: 83/7, v: 215/28}
Correct? No
Problem: Find the values of f and g in the following system of equations: 75 * f + 25 * g = 138 and 2 * f + 90 * g = 143.
InternLM-Math Base 7B:
Reasoning: 75f+25g=138 2f+90g=143 2f+90g-90g=143-90g 2f=53g 2f/2=53g/2 f=53g/2 2f/2+25g=138/2 53g/2+25g=69 78g/2=69 78g=138 78g/78=138/78 g=138/78 2f+90g/2=143/2 2f+90g/2=71.5 2f+45g=71.5 2f/2+45g/2=71.5/2 2f/2+22.5g=35.75 2f/2=35.75-22.5g 2f/2=13.25-11g f/2=6.625-5.5g 2f/2+5.5g=6.625 2f/2+5.5g-5.5g=6.625-5.5g 2f/2=1.125 f=1.125*2=2.25 2.25*2+5.5*138/78= 4.5+5.5*138/78 4.5+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4.5+1.5=6 2.25*2+5.5*19/78 4
Expected answer: {f: 1769/1340, g: 10449/6700}
Correct? No
Problem: Solve the following system of equations for variables y and n: the first equation is 194 = 4 * y + 14 * n and the second equation is 7 = 65 * n - 79 * y.
InternLM-Math Base 7B:
Reasoning: 194 = 4 * y + 14 * n ⇒ 194- 4 * y = 14 * n ⇒ 4 * y + 7 = 14 * n ⇒ 4 * y + 7 = 65 * n - 79 * y ⇒ 4 * y + 7 + 79 * y = 65 * n ⇒ 83 * y = 65 * n - 7 ⇒ 83 * y = 65 * 7 - 7 ⇒ 83 * y = 448 ⇒ 83 * y/83 = 448/83 ⇒ y = 5 ⇒ 5 = 65 * n - 79 * 5 ⇒ 5 = 65 * n - 395 ⇒ 5 + 395 = 65 * n ⇒ 400 = 65 * n ⇒ 400/65 = 65 * n/65 ⇒ 6 = n ⇒ 5 = 65 * 6 - 79 * 5 ⇒ 5 = 390 - 395 ⇒ 5 = -5 ⇒ 5+5 = -5+5 ⇒ 10 = 0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0 ⇒ 10/0 = 0/0
Expected answer: {n: 7677/683, y: 6256/683}
Correct? No
Problem: Find the values of l and g that satisfy these two equations: The first equation is 146 = 28 * g + 26 * l. The second equation is 6 = 41 * l - 53 * g.
InternLM-Math Base 7B:
Reasoning: 6 = 41 * l - 53 * g -6 = - 41 * l + 53 * g -6 = 53 * ( 1/53 * g) - 41 * (1/41 * l) -6 = 1 * (53 * 1/53 * g) - 1 * (41 * 1/41 * l) -6 = 1 * ( 1 * 53 * 1/53 * g) - 1 * ( 1 * 41 * 1/41 * l) -6 = 1 * 1 * 53 * 1/53 * g - 1 * 1 * 41 * 1/41 * l -6 = 1 * 1 * 1 * 53 * 1/53 * g - 1 * 1 * 1 * 41 * 1/41 * l -6 = 1 * 1 * 1 * 1 * 53 * 1/53 * g - 1 * 1 * 1 * 1 * 41 * 1/41 * l -6 = 1 * 1 * 1 * 1 * 1 * 53 * 1/53 * g - 1 * 1 * 1 * 1 * 1 * 41 * 1/41 * l -6 = 1 * 1 * 1 * 1 * 1 * 1 * 53 * 1/53 * g - 1 * 1 * 1 * 1 * 1 * 1 * 41 * 1/41 * l -6 = 1 * 1 * 1 * 1 * 1 * 1 * 1 * 53 * 1/53 * g - 1 * 1 * 1 * 1 * 1 * 1 * 1 * 41 * 1/41 * l -6 = 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 53 * 1/53 * g - 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 41 * 1/41 * l -6 = 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 53 * 1/53 * g - 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 41 * 1/41 * l -6 = 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 53 * 1/53 * g - 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 41 * 1/41 * l -6 = 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 53 * 1/53 * g - 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 41 * 1/41 * l -6 = 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 53 * 1/53 * g - 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 41 * 1/41 * l -6 = 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 53 * 1/53 * g - 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 41 * 1/41 * l -6 = 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 53 * 1/53 * g - 1 * 1 *
Expected answer: {g: 2915/1263, l: 3953/1263}
Correct? No
Problem: Consider the following system of equations: 1) 20 * p + 56 * y = 90 2) 89 * p + 7 * y = 98 Resolve this system and find the values of p and y.
InternLM-Math Base 7B:
1) 20 * p + 56 * y = 90 2) 89 * p + 7 * y = 98 p = <<p=3>>3 y = <<y=1>>1 ### Answer: 3, 1
Expected answer: {p: 347/346, y: 3025/2422}
Correct? No
Problem: Given the system of equations: 72*k - 22*d = 17 and 6*d +69*k = 96, find the values of variables k and d.
InternLM-Math Base 7B:
Reasoning: 6d+69k=96 -69k-6d=96-69k -69k-6d=27 -6d=27-69k -6d=27-6d+6d-69k -6d=27-6d-6d-69k -6d-6d=27-6d-69k -12d=27-69k -12d-12d=27-69k-12d -12d-12d=27-12d-69k -24d=27-12d-69k -24d-12d=27-12d-69k-12d -36d=27-69k-12d -36d-12d=27-69k-12d-12d -48d=27-69k-12d-12d -48d-12d=27-69k-12d-12d-12d -60d=27-69k-12d-12d-12d -60d-12d=27-69k-12d-12d-12d-12d -72d=27-69k-12d-12d-12d-12d -72d-12d=27-69k-12d-12d-12d-12d-12d -84d=27-69k-12d-12d-12d-12d-12d -84d-12d=27-69k-12d-12d-12d-12d-12d-12d -96d=27-69k-12d-12d-12d-12d-12d-12d -96d-12d=27-69k-12d-12d-12d-12d-12d-12d-12d -108d=27-69k-12d-12d-12d-12d-12d-12d-12d -108d-12d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d -120d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d -120d-12d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d-12d -132d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d-12d -132d-12d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d -144d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d -144d-12d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d -156d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d -156d-12d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d -168d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d -168d-12d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d -180d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d-12d -180d-12d=27-69k-12d-12d-12d-12d-12d-12d-12d-12d-12d-12
Expected answer: {d: 1913/650, k: 369/325}
Correct? No
Problem: Solve the following system of equations to find the values of d and h: 73 * h - 33 * d = 48 10 * d + 14 * h = 91
InternLM-Math Base 7B:
Expected answer: {d: 5971/1192, h: 3483/1192}
Correct? No
Problem: Solve the following system of equations for the values of q and e: 1) 43 * q - 44 * e = 29 2) 30 * q + 43 * e = 130
InternLM-Math Base 7B:
Reasoning:
Expected answer: {e: 4720/3169, q: 6967/3169}
Correct? No
Problem: Find the values of r and a in the following system of equations: 53 = ((89 * r) - (74 * a)) 109 = ((37 * a) + (6 * r))
InternLM-Math Base 7B:
Reasoning: 53 = ((89 * r) - (74 * a)) 109 = ((37 * a) + (6 * r)) 37a + 6r = 109 89r - 74a = 53 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37a 6r = 109 - 37
Expected answer: {a: 9383/3737, r: 271/101}
Correct? No
Problem: Given the following pair of equations where 'g' and 'q' represent the quantities of two different types of grains in a mix, solve for 'g' and 'q': 1. The sum of the weights of 42 units of 'g' and 12 units of 'q' equals 169 kg. 2. The weight of 12 units of 'q' minus the weight of 50 units of 'g' results in 19 kg.
InternLM-Math Base 7B:
Reasoning: 1. 42g + 12q = 169 2. 12q - 50g = 19 Solve the first equation for 'g' in terms of 'q' to get 42g = 169 - 12q. Substituting this value of 42g into the second equation, we have 12q - 50(169-12q) = 19. Solving for 'q' we get 6q = 19. Therefore 2q = 19/6. Substituting this value of 2q into the first equation, we have 42g = 169 - 12(19/6) = 169 - 19. Therefore 42g = 150. It follows that 3g = 150/42 = 5. Therefore g = 5/3. It follows that 2q = 19/6 = 5/3. Therefore q = 5/3.
Expected answer: {g: 75/46, q: 578/69}
Correct? No
Problem: Find the values of s and v for the following system of equations: 37 * s - 11 * v = 54 82 * s - 62 * v = 41
InternLM-Math Base 7B:
Reasoning: 37 * s - 11 * v = 54 ⇒ 37 * s = 11 * v + 54 ⇒ 3 * 37 * s = 3 * 11 * v + 3 * 54 ⇒ 111 * s = 33 * v + 162 ⇒ 111 * s - 33 * v = 162 ⇒ 3 * 37 * s - 3 * 11 * v = 3 * 54 ⇒ 3 * 82 * s - 3 * 62 * v = 3 * 41 ⇒ 246 * s - 186 * v = 123 ⇒ 2 * 123 = 246 * s - 186 * v ⇒ 246 * s - 186 * v = 246 ⇒ 2 * 123 = 246 ⇒ 2 * 123 = 2 * 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123 ⇒ 123 = 123
Expected answer: {s: 2897/1392, v: 2911/1392}
Correct? No
Problem: Based on the following two equations, find the values for c and z: The first equation is 41 * c + 65 * z = 151 The second equation is 78 * z - 48 * c = 48.
InternLM-Math Base 7B:
Reasoning: 78 * z - 48 * c = 48 78 * z = 48 + 48 * c z = 48 + 48 * c/78 z = 48 + 2 * c/3 z = 2/3 * c + 48 41 * c + 65 * z = 151 41 * c + 65 * (2/3 * c + 48) = 151 41 * c + 65 * 2/3 * c + 65 * 48 = 151 (41 + 65 * 2/3) * c + 65 * 48 = 151 (41 + 65 * 2/3) * c = 151 - 65 * 48 (41 + 65 * 2/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 * 65/3) * c = 151 - 65 * 48 (41 + 2 *
Expected answer: {c: 37/27, z: 512/351}
Correct? No
Problem: Given the following system of equations: 60 * c - 91 * i = 7 7 * i + 76 * c = 148 What are the values of c and i?
InternLM-Math Base 7B:
Reasoning: 60 * c - 91 * i = 7 7 * i + 76 * c = 148 c = 0.8 i = 0.8 ### Answer: 0.8, 0.8
Expected answer: {c: 1931/1048, i: 2087/1834}
Correct? No
Problem: Find the values of e and v that satisfy the following two simultaneous linear equations: 1) 71*v - 37*e = 69 2) 41*e + 76*v = 184
InternLM-Math Base 7B:
Reasoning: 71*v - 37*e = 69 41*e + 76*v = 184 Multiply the first equation by 2, and the second by 3. 1) 142*v - 74*e = 138 2) 123*e + 228*v = 552 Add the first and second equations. 1) 165*e + 300*v = 690 2) 123*e + 228*v = 552 Subtract the second equation from the first. 1) 42*e + 72*v = 138 2) 123*e + 228*v = 552 Multiply the first equation by 3. 1) 126*e + 216*v = 414 2) 123*e + 228*v = 552 Subtract the first equation from the second. 1) 3*e - 12*v = 138 2) 123*e + 228*v = 552 Multiply the first equation by 4. 1) 12*e - 48*v = 552 2) 123*e + 228*v = 552 Subtract the first equation from the second. 1) 111*e = 0 2) 123*e + 228*v = 552 Subtract 111e from the second equation. 1) 111*e = 0 2) 12*v = 552 Divide the first equation by 111. 1) 111*e = 0 2) 12*v = 552 Divide the second equation by 12. 1) 111*e = 0 2) v = 46.5 Subtract 111e from the first equation. 1) 111*e = 0 2) 12*v = 552 Divide the first equation by 12. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) 12*v = 552 Divide the second equation by 12. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Divide the first equation by 111. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0 2) v = 46.5 Subtract 46.5v from the second equation. 1) 111*e = 0
Expected answer: {e: 7820/5723, v: 9637/5723}
Correct? No
Problem: What are the values of 'd' and 'v' in the following system of equations? The sum of 25 times 'v' and 69 times 'd' equals 113. The sum of 26 times 'd' and 42 times 'v' equals 85.
InternLM-Math Base 7B:
Reasoning: The first equation is 25v+69d=113. The second equation is 26d+42v=85. The sum of 25v+69d=113 and 25v-25v=0 is 25v+69d-25v=113-0. The sum of 26d+42v=85 and 0-26d=0 is 26d+42v-26d=85-0. The sum of 25v+69d-25v=113-0 and 26d+42v-26d=85-0 is 25v+69d-25v+26d+42v-26d=113-0+85-0. 25v+25v+26d-26d+69d+42v=113+85. 25v+25v-25v+26d-26d+42v+69d=113+85. 25v+26d+42v+69d=113+85. 25v+26d+42v+69d-0=113+85-0. 25v+26d+42v+69d-0=113+85. 25v+26d+42v+69d=198. 25v+26d+42v+69d-0-0=198-0-0. 25v+26d+42v+69d-0-0=198. 25v+26d+42v+69d=198. 25v+26d+42v+69d-0-0-0=198-0-0-0. 25v+26d+42v+69d-0-0-0=198. 25v+26d+42v+69d=198. 25v+26d+42v+69d-0-0-0-0=198-0-0-0. 25v+26d+42v+69d-0-0-0-0=198. 25v+26d+42v+69d=198. 25v+26d+42v+69d-0-0-0-0-0=198-0-0-0-0. 25v+26d+42v+69d-0-0-0-0-0=198. 25v+26d+42v+69d=198. 25v+26d+42v+69d-0-0-0-0-0-0=198-0-0-0-0-0. 25v+26d+42v+69d-0-0-0-0-0-0=198. 25v+26d+42v+69d=198. 25v+26d+42v+69d-0-0-0-0-0-0-0=198-0-0-0-0-0-0. 25v+26d+42v+69d-0-0-0-0-0-0-0=198. 25v+26d+42v+69d=198. 25v+26d+42v+69d-0-0-0-0-0-0-0-0=198-0-0-0-0-0-0-0. 25v+26d+42v+69d-0-0-0-0-0-0-0-0=198. 25v+26d+42v+69d=198. 25v+26d+42v+69d-0-0-0-0-0-0-0-0-0=198-0-0-0-0-0-0-0-0. 25v+26d+42v+69d-0-0-0-0-0-0-0-0-0=198. 25v+26d+42v+69d=198. 25v+26d+42v+69d-0-0-0-0-0-0-0-0-0-0=198-0-0-0-0-0-0-0-0-0. 25v+26d+42v+69d-0-0-0-0-0-0-0-0-0-0=198. 25v+26d+42v+69d=198. 25v+26d+42
Expected answer: {d: 2621/2248, v: 2927/2248}
Correct? No
Problem: Solve the following equations for g and z: 43 * z - 91 * g = 33 72 * g - 3 * z = 68
InternLM-Math Base 7B:
Reasoning: 43 * z - 91 * g = 33 43z - 91g = 33 - 43z + 91g = 33 - 43z = 33 + 91g - 43z = 124g - 43z/43 = 124g/43 - 1z = 2.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g - 1z = 2g + 0.9g -
Expected answer: {g: 3023/2823, z: 8564/2823}
Correct? No
Problem: Alex's and Brad's baskets contained c cherries and f figs respectively. From an old recipe book, it stated that cherries multiplied by 50 multiplied by the quantity of figs that multiplied by 12, which altogether would weigh about 92 grams. Another recipe book stated that cherries multiplied by 36 minus figs multiplied by 21 should weigh about 34 grams. Can you find the quantity of cherries (c) and figs (f)? Use the following system of equations to solve: 50c + 12f = 92 36c - 21f = 34.
InternLM-Math Base 7B:
Reasoning: 50c + 12f = 92 36c - 21f = 34 Multiply the first equation by 3 to get 150c + 36f = 276 Multiply the second equation by 3 to get 108c - 63f = 102 Add the two equations to get 258c = 378 c = 1.5 Substitute 1.5 for c in the first equation to get 12f = 25.5 f = 2.125 ### Answer: 1.5, 2.125
Expected answer: {c: 30/19, f: 62/57}
Correct? No
Problem: Here are the equations you'll need to solve (remember, the goal is to find the values of u and d): 1) 87u - 75d = 7 2) 85d - 82u = 54
InternLM-Math Base 7B:
You can use the following values to find the value of u and d: u = <<u=3>>3, d = <<d=8>>8
Expected answer: {d: 5272/1245, u: 929/249}
Correct? No
Problem: Bill is trying to decipher a secret code. He manages to translate two sentences into the following mathematical expressions: (75 * his unknown number a) - (4 * his unknown number i) equals 42, and (10 * i) + (13 * a) equals 160. Using these equations, can you figure out the values of i and a for him?
InternLM-Math Base 7B:
Reasoning: 75a - 4i = 42 10i + 13a = 160 10i + 13a = 160 10i = 160 - 13a 10i = 160 - 13a 10i = 160 - 13a 10i/10 = 160/10 - 13a/10 10i/10 = 16/1 - 13a/10 1i/1 = 1.6 - 1.3a i/1 = 1.6/1 - 1.3a i/1 = 1.6 - 1.3a i = 1.6 - 1.3a i = 1.6 - 1.3a 10i = 10(1.6) - 10(1.3a) 10i = 16 - 10(1.3a) 10i = 16 - 13a 10i/10 = 16/10 - 13a/10 1i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a 10i/10 = 10(1.6) - 10(1.3a) 10i/10 = 16 - 10(1.3a) 10i/10 = 16 - 13a 1i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a 10i/10 = 10(1.6) - 10(1.3a) 10i/10 = 16 - 10(1.3a) 10i/10 = 16 - 13a 1i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a 10i/10 = 10(1.6) - 10(1.3a) 10i/10 = 16 - 10(1.3a) 10i/10 = 16 - 13a 1i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a 10i/10 = 10(1.6) - 10(1.3a) 10i/10 = 16 - 10(1.3a) 10i/10 = 16 - 13a 1i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a 10i/10 = 10(1.6) - 10(1.3a) 10i/10 = 16 - 10(1.3a) 10i/10 = 16 - 13a 1i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a 10i/10 = 10(1.6) - 10(1.3a) 10i/10 = 16 - 10(1.3a) 10i/10 = 16 - 13a 1i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a 10i/10 = 10(1.6) - 10(1.3a) 10i/10 = 16 - 10(1.3a) 10i/10 = 16 - 13a 1i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a i/1 = 1.6 - 1.3a 10i/10 = 10(1.6) - 10(1.3a) 10i/10 = 16 - 10(1.3a) 10i/10 = 16 - 13a 1i/1 = 1.6 - 1.
Expected answer: {a: 530/401, i: 5727/401}
Correct? No
Problem: Solve the following system of equations for the values of p and c: 37 * p + 74 * c = 183 27 * c - 18 * p = 13
InternLM-Math Base 7B:
Reasoning: 37 * p + 74 * c = 183 27 * c - 18 * p = 13 3(27 * c - 18 * p) = 3(13) 81 * c - 54 * p = 39 3(37 * p + 74 * c) = 3(183) 111 * p + 222 * c = 549 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 =
Expected answer: {c: 3775/2331, p: 3979/2331}
Correct? No
Problem: Determine the values of k and p from the following system of equations: (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105.
InternLM-Math Base 7B:
You are correct.
Expected answer: {k: 1871/879, p: 1273/586}
Correct? No
Problem: Consider the following pair of equations. 1. 75v - 69f = 14 2. 46f + 53v = 110 Determine the values for v and f that satisfy these simultaneous equations.
InternLM-Math Base 7B:
Reasoning: 1. 75v - 69f = 14 2. 46f + 53v = 110 3. 1. + 2. = 2. + 1. = 0. 75v - 69f = 14 46f + 53v = 110 121v = 124 46f = 14 121v = 124 46f = 14 1. 121v = 124 2. 46f = 14 3. 121v = 46f 3. 124 = 14 4. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3
Expected answer: {f: 7508/7107, v: 358/309}
Correct? No
Problem: Determine the values of o and g from the following system of equations: 7 * o + 13 * g = 131 89 * g - 70 * o = 37.
InternLM-Math Base 7B:
Reasoning: 7 * o + 13 * g = 131 89 * g - 70 * o = 37 7 * o + 13 * g = 131 7 * o = 131 - 13 * g o = 131/7 - 13/7 * g o = 19 - 13/7 * g 89 * g - 70 * o = 37 89 * g - 70 * (19 - 13/7 * g) = 37 89 * g - 70 * 19 + 70 * 13/7 * g = 37 89 * g - 1430 + 70 * 13/7 * g = 37 89 * g - 1430 + 70/7 * 13 * g = 37 89 * g - 1430 + 910/7 * g = 37 89 * g - 1430 + 130/7 * g = 37 (89 + 130/7) * g - 1430 = 37 (89 + 130/7) * g = 37 + 1430 (89 + 130/7) * g = 1467 (89 + 130/7) * g/ (89 + 130/7) = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467/ (89 + 130/7) g = 1467
Expected answer: {g: 449/73, o: 3726/511}
Correct? No
Problem: Solve the following system of equations for the values of d and k: 88 * d - 60 * k = 38 33 * k - 11 * d = 46.
InternLM-Math Base 7B:
Reasoning: 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38 33 * k - 11 * d = 46 88 * d - 60 * k = 38
Expected answer: {d: 669/374, k: 203/102}
Correct? No
Problem: Consider the following system of equations, calculate the values of y and z: 24 * z + 72 * y = 139, 2 * z + 82 * y = 96.
InternLM-Math Base 7B:
Reasoning: 2*24*z+2*72*y=2*139, 2*2*z+2*82*y=2*96, 2*24*z+2*72*y-2*2*z-2*82*y=2*139-2*96, 2*24*z-2*2*z+2*72*y-2*82*y=2*139-2*96, 2*22*z+2*-50*y=2*43, 2*(11*z-25*y)=2*43, 11*z-25*y=43, 11*z-25*y-11*z-25*y=43-11*z-25*y, -25*y-25*y=43-11*z-11*z, -50*y=43-11*z-11*z, -50*y=43-11*(z+z), -50*y=43-11*2z, -50*y=43-22z, -50*y+50*y=43-22z+50*y, 50*y-50*y=43-22z+50*y, 0=43-22z+50*y, 0-43-0=43-22z+50*y-0, -43=43-22z+50*y, -43-43-43=43-22z+50*y-43-43, -43-43-43=43-22z+50*y-43-43-43, -43-43-43-43-43-43=43-22z+50*y-43-43-43-43, -43-43-43-43-43-43-43-43-43=43-22z+50*y-43-43-43-43-43, -43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43-43
Expected answer: {y: 1013/912, z: 2243/912}
Correct? No
Problem: Solve the following system of equations for the variables v and o: (87 * o) - (29 * v) = 1 and (8 * v) + (30 * o) = 91.
InternLM-Math Base 7B:
Reasoning: (8 * v) + (30 * o) = 91 ⇒ 8 * v = 91 - 30 * o ⇒ v = 11 - 3.75 * o ⇒ v = 11 - 3.75 * o ⇒ 87 * o - 29 * v = 1 ⇒ 87 * o - 29 * (11 - 3.75 * o) = 1 ⇒ 87 * o - 29 * 11 + 29 * 3.75 * o = 1 ⇒ 87 * o - 319 + 3.75 * 29 * o = 1 ⇒ 87 * o - 319 + 3.75 * 29 * o = 1 ⇒ 0.25 * o = 0.25 ⇒ o = 1 ⇒ v = 11 - 3.75 * 1 ⇒ v = 8 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v = 8 ⇒ o = 1 ⇒ o = 1 ⇒ v =
Expected answer: {o: 2647/1566, v: 2629/522}
Correct? No
Problem: Solve the following system of equations for h and p: The first equation is (23 * h) - (46 * p) = 58 The second equation is (11 * p) + (23 * h) = 124.
InternLM-Math Base 7B:
Reasoning: The first equation is (23 * h) - (46 * p) = 58. The second equation is (11 * p) + (23 * h) = 124. Solve the first equation for h. h = 58 + (46 * p) / 23. Substitute 58 + (46 * p) / 23 for h in the second equation. (11 * p) + (23 * (58 + (46 * p) / 23)) = 124. Solve the second equation for p. p = 124 - (23 * 58) / 11. p = 124 - 58. p = 66. Substitute 66 for p in the first equation. (23 * h) - (46 * 66) = 58. Solve the first equation for h. h = 58 + (46 * 66) / 23. h = 58 + 46. h = 104. ### Answer: 66, 104
Expected answer: {h: 2114/437, p: 22/19}
Correct? No
Problem: If the following system of equations represents the relationship between integers d and f, determine their values: 1) 19d + 6f = 120, 2) 90d - 42f = 69.
InternLM-Math Base 7B:
Reasoning: 1) 19d + 6f = 120, 2) 90d - 42f = 69. Solve 1) for f: 6f = 120-19d, f = 20-3d. Solve 2) for f: 42f = 69-90d, f = 69/42-90d/42. f = 20-3d = 69/42-90d/42. Solve for d: 3d-90d/42 = 20-69/42. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43. d = 20-69/42-3d/43.
Expected answer: {d: 909/223, f: 3163/446}
Correct? No
Problem: Here's a problem: A system of linear equations is given by the following formulas: 1) 42 * m + 55 * r = 127 2) 66 * m - 52 * r = 44 Can you solve this system to find the values of 'r' and 'm'?
InternLM-Math Base 7B:
1) 42 * m + 55 * r = 127 2) 66 * m - 52 * r = 44
Expected answer: {m: 1504/969, r: 363/323}
Correct? No
Problem: Determine the values of n and w that satisfy the following system of linear equations simultaneously: 31n + 64w = 120 57w + 71n = 173
InternLM-Math Base 7B:
Reasoning: 31n + 64w = 120 ⇒ 64w = 120 – 31n ⇒ w = (120 – 31n)/64 ⇒ 64w = 120 – 31n ⇒ 57w + 71n = 173 ⇒ 57(120 – 31n)/64 + 71n = 173 ⇒ 57(120 – 31n) + 71n(64) = 173(64) ⇒ 6840 – 1911n + 4464n = 10992 ⇒ 1911n – 4464n = 10992 – 6840 ⇒ 2553n = 3052 ⇒ n = 3052/2553 ⇒ 31n + 64w = 120 ⇒ 31(3052/2553) + 64w = 120 ⇒ 64w = 120 – 95008/2553 ⇒ w = 120 – 95008/2553 ⇒ 64w = 64(120 – 95008/2553) ⇒ 64w = 7600 – 95008 ⇒ 64w = – 85808 ⇒ w = – 85808/64 ⇒ 57w + 71n = 173 ⇒ 57( – 85808/64) + 71n = 173 ⇒ 71n = 173 – 52551 ⇒ n = 173 – 52551 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n + 64w = 120 ⇒ 31n
Expected answer: {n: 4232/2777, w: 3157/2777}
Correct? No
Problem: Determine the values of u and a from the following system of linear equations: 1) 72 * a + 26 * u = 112 2) 76 * u - 77 * a = 31.
InternLM-Math Base 7B:
1) 72 * a + 26 * u = 112 2) 76 * u - 77 * a = 31
Expected answer: {a: 3853/3737, u: 5428/3737}
Correct? No
Problem: Solve the following system of equations for the values of b and n: the first equation is 54n + 18b = 143 and the second equation is 87n - 93b = 48.
InternLM-Math Base 7B:
Reasoning: 87n - 93b = 48 87n+18b-18b-93b = 48-18b 87n+18b-93b = 48-18b 87n-75b = 48-18b 87n-75b+18b = 48-18b+18b 87n-57b = 48 54n+18b-54n-18b = 48-54n-18b 54n+18b-54n-18b = 48 0-36b = 48 -36b = 48 b = 48/-36 b = -4/3 87n-75b = 48 87n-75(-4/3) = 48 87n-100/3 = 48 87n-100/3+3/3 = 48+3/3 87n-3-100/3 = 48+3-3 87n-3-100/3 = 45 87n-3-100/3+3/3 = 45+3/3 87n-3-3-100/3 = 45+3-3 87n-3-3-100/3 = 42 87n-3-3-100/3+3/3 = 42+3/3 87n-3-3-3-100/3 = 42+3-3 87n-3-3-3-100/3 = 39 87n-3-3-3-100/3+3/3 = 39+3/3 87n-3-3-3-3-100/3 = 39+3-3 87n-3-3-3-3-100/3 = 36 87n-3-3-3-3-100/3+3/3 = 36+3/3 87n-3-3-3-3-3-100/3 = 36+3-3 87n-3-3-3-3-3-100/3 = 33 87n-3-3-3-3-3-100/3+3/3 = 33+3/3 87n-3-3-3-3-3-3-100/3 = 33+3-3 87n-3-3-3-3-3-3-100/3 = 30 87n-3-3-3-3-3-3-100/3+3/3 = 30+3/3 87n-3-3-3-3-3-3-3-100/3 = 30+3-3 87n-3-3-3-3-3-3-3-100/3 = 27 87n-3-3-3-3-3-3-3-100/3+3/3 = 27+3/3 87n-3-3-3-3-3-3-3-3-100/3 = 27+3-3 87n-3-3-3-3-3-3-3-3-100/3 = 24 87n-3-3-3-3-3-3-3-3-100/3+3/3 = 24+3/3 87n-3-3-3-3-3-3-3-3-3-100/3 = 24+3-3 87n-3-3-3-3-3-3-3-3-3-100/3 = 21 87n-3-3-3-3-3-3-3-3-3-100/3+3/3 = 21+3/3 87n-3-3-3-3-3-3-3-3-3-3-100/3 = 21+3-3 87n-3-3-3-3-3-3-3-3-3-3-100/3 = 18 87n-3-3-3-3-3-3-3-3-3-3-100/3+3/3 = 18+3/3 87n-3-3-3-3-3-3-3-3-3-3-3-100/3 = 18+3-3 87n-3-3-3-3-3-
Expected answer: {b: 3283/2196, n: 4721/2196}
Correct? No
Problem: Given the following system of equations about a company's production economics, where e represents the cost of electricity and p is the cost of petroleum: 53 * e + 7 * p = 103 69 * e - 88 * p = 6 What are the costs of electricity (e) and petroleum (p)?
InternLM-Math Base 7B:
53 * e + 7 * p = 103 69 * e - 88 * p = 6 7 * 69 * e - 7 * 88 * p = 6 * 7 7 * 69 * e - 7 * 88 * p = 42 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p 7 * 69 * e = 42 + 7 * 88 * p
Expected answer: {e: 9106/5147, p: 6789/5147}
Correct? No
Problem: Consider the following pair of linear equations. First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Find the values of p and s that satisfy both equations.
InternLM-Math Base 7B:
You are a mathematics teacher that solves all problems correctly and explains your reasoning. Write your final answer in the last line of your response. The last line should always be formatted as follows: "### Answer: <<your final answer here.>>".
Expected answer: {p: 1169/750, s: 126/125}
Correct? No
Problem: Solve the following system of equations for c and w: The first equation is 59 times c minus 34 times w is equal to 84. The second equation is 11 times c plus 42 times w is equal to 98.
InternLM-Math Base 7B:
Reasoning: 11c+42w=98 59c-34w=84 -11c-11c -42w-42w -11c-42w=14 -1(11c+42w=98) -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -11c-42w=14 -
Expected answer: {c: 1715/713, w: 2429/1426}
Correct? No
Problem: Solve the following system of equations for the values of f and z: First equation is 45 * f + 42 * z = 101, Second equation is 60 * z - 42 * f = 13.
InternLM-Math Base 7B:
Reasoning:
Expected answer: {f: 919/744, z: 1609/1488}
Correct? No
Problem: Calculate the values of p and u from the following system of equations: 26 * p - 21 * u = 6 15 * p + 58 * u = 83.
InternLM-Math Base 7B:
Reasoning: The first equation is 6 = 26p - 21u. The second equation is 83 = 15p + 58u. Multiply the first equation by 58 and the second by 21. 1248p - 1038u = 348 1710p + 1218u = 1823 Add the two equations together. 1248p - 1038u + 1710p + 1218u = 348 + 1823 2958p = 2171 p = 2171/2958 p = 0.733 Multiply the first equation by 15 and the second by 26. 390p - 315u = 90 390p + 1348u = 2198 Add the two equations together. 390p - 315u + 390p + 1348u = 90 + 2198 1280p = 2288 u = 2288/1280 u = 1.78 ### Answer: 0.733 1.78
Expected answer: {p: 2091/1823, u: 2068/1823}
Correct? No
Problem: Solve for the values of n and s using these two simultaneous equations: 1) 92 * n - 38 * s = 62 2) 59 * n + 8 * s = 75
InternLM-Math Base 7B:
Reasoning: 92 * n - 38 * s = 62 59 * n + 8 * s = 75
Expected answer: {n: 1673/1489, s: 1621/1489}
Correct? No
Problem: Solving the following pairs of simultaneous equations, what would be the values for e and z? The equations are: 87 * z - 35 * e = 63 and 81 * z + 58 * e = 154.
InternLM-Math Base 7B:
Expected answer: {e: 2765/2627, z: 9044/7881}
Correct? No
Problem: To find the values of h and t, solve the following system of simultaneous linear equations: (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18.
InternLM-Math Base 7B:
Reasoning: The solution to the system of equations is: t = 3 and h = 2. ### Answer: 3, 2
Expected answer: {h: 481/214, t: 108/107}
Correct? No
Problem: Solve the following system of linear equations to find the values of b and o: ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85.
InternLM-Math Base 7B:
Reasoning: ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85 b = <<b>> o = <<o>>
Expected answer: {b: 6505/3729, o: 1625/1243}
Correct? No
Problem: Solve the following system of equations to find the values of p and q: 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177.
InternLM-Math Base 7B:
Reasoning: 67 * q - 80 * p = 65 6 * q + 5 * p = 177 6(65) + 5(177) = 6(67 * q - 80 * p) + 5(6 * q + 5 * p) 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) * q + 5(5) * p 6(65) + 5(177) = 6(65) * q - 6(80) * p + 5(6) *
Expected answer: {p: 11469/815, q: 2897/163}
Correct? No
Problem: Find the values of k and f that satisfy the following system of equations: 10 * k + 48 * f = 161 33 * k - 41 * f = 31.
InternLM-Math Base 7B:
Reasoning: 10 * k + 48 * f = 161 10 * k = 161-48 * f 10 * k = 161-10 * 3 * f 10 * k = 161-10 * 3 * 3 10 * k = 161-10 * 9 10 * k = 161-90 10 * k = 71 k = 7.1 10 * 7.1 + 48 * f = 161 10 * 7.1 = 161-48 * f 10 * 7.1 = 161-10 * 3 * f 10 * 7.1 = 161-10 * 3 * 3 10 * 7.1 = 161-10 * 9 10 * 7.1 = 161-90 10 * 7.1 = 71 f = 3 10 * 7.1 + 48 * 3 = 161 10 * 7.1 = 161-48 * 3 10 * 7.1 = 161-10 * 3 * 3 10 * 7.1 = 161-10 * 9 10 * 7.1 = 161-90 10 * 7.1 = 71 10 * 7.1 = 71 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.1 7.1 = 7.
Expected answer: {f: 5003/1994, k: 8089/1994}
Correct? No
Problem: Solve the following system of equations for the values of l and n: The first equation is 31 = 58 * l - n The second equation is 103 = n + 73 * l
InternLM-Math Base 7B:
Reasoning: 31 = 58 * l - n 31 + n = 58 * l 103 = 58 * l + n 103 - 58 * l = n n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l n = 103 - 58 * l
Expected answer: {l: 134/131, n: 3711/131}
Correct? No
Problem: Find the values of y and j that satisfy the following system of equations: 29y - 28j = 39 25y + 37j = 116
InternLM-Math Base 7B:
Reasoning: 29y - 28j = 39 25y + 37j = 116
Expected answer: {j: 2389/1773, y: 4691/1773}
Correct? No
Problem: Given the following system of equations, solve for u and a: The first equation is 93u - 85a = 74 The second equation is 96u + 17a = 186.
InternLM-Math Base 7B:
Reasoning: 93u - 85a = 74 96u + 17a = 186 -85a - 17a = -85a 93u - 102a = 74-102a 93u = 74-102a+102a 93u = 74 u = 74/93 u = <<74/93=0.8>>0.8 96u+17a=186 <<0.8*96=78.4>>78.4+17a=186 -17a=186-78.4 -17a=<<108.6>>108.6 a=<<-108.6/17>>-6.4 ### Answer: 0.8, -6.4
Expected answer: {a: 3398/3247, u: 1004/573}
Correct? No
Problem: Given the following pair of simultaneous equations, please find out the values of u and g: 97 * u - 61 * g = 15 85 * u + 23 * g = 186
InternLM-Math Base 7B:
Reasoning: 97u - 61g = 15 85u + 23g = 186 2(97u - 61g) = 2(15) 2(85u + 23g) = 2(186) 194u - 122g = 30 170u + 46g = 372 194u - 122g + 170u + 46g = 30 + 372 364u = 402 u = 402/364 = 1.1 g = 1.1*61/97 = 0.6 ### Answer: u = 1.1, g = 0.6
Expected answer: {g: 1863/824, u: 1299/824}
Correct? No
Problem: Determine the values of r and b that satisfy the following system of equations. The first equation is (17 * r) + (67 * b) = 103. The second equation is (85 * r) + (67 * b) = 187.
InternLM-Math Base 7B:
17r + 67b = 103 85r + 67b = 187 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103 17r + 67b 17r + 67b = 103
Expected answer: {b: 82/67, r: 21/17}
Correct? No
Problem: Given the following system of equations, solve for the values of t and n: 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126.
InternLM-Math Base 7B:
Reasoning: 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n = 41 + 54 * t 2. 30 * n = 126 - 38 * t 3. 1. 85 * n
Expected answer: {n: 4181/2425, t: 948/485}
Correct? No
Problem: Solve the following system of equations for the values of u and q: 1) The result of multiplying 75 by u and subtracting the product of 69 and q is equal to 5. 2) The sum of the product of 48 and u and the product of 25 and q is 140.
InternLM-Math Base 7B:
Expected answer: {q: 180/91, u: 515/273}
Correct? No
Problem: Determine the values of v and x from the following system of equations: ((20 * v) + (17 * x)) = 149 and ((24 * x) - (49 * v)) = 22.
InternLM-Math Base 7B:
Reasoning: The value of v is <<v=3>>. The value of x is <<x=2>>.
Expected answer: {v: 3202/1313, x: 7741/1313}
Correct? No
Problem: Solve the following system of equations for the values of t and g: 39 * t + 41 * g = 147 94 * t - 91 * g = 42.
InternLM-Math Base 7B:
Reasoning: 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g = 42 39t + 41g = 147 94t - 91g
Expected answer: {g: 12180/7403, t: 15099/7403}
Correct? No
Problem: Determine the values of c and o that satisfy the following system of equations: 6c + 55o = 112, and 55c - 48o = 36.
InternLM-Math Base 7B:
Reasoning: 6c + 55o = 112 6c = 112 - 55o 6c = 36 + 55o 6c = 6o + 36 6c - 6o = 36 6c - 6o = 6o - 6o 6c = 6o 6c/6 = 6o/6 1c = 1o c = o ### Answer: 1
Expected answer: {c: 7356/3313, o: 5944/3313}
Correct? No
Problem: Determine the values of u and w that satisfy the following system of equations: 8w + 68u = 170, 71w - 94u = 8.
InternLM-Math Base 7B:
Reasoning: 8u = 170 - 8w. 8u = 8. u = 1. 8w = 170 - 8u. 8w = 160. w = 20.
Expected answer: {u: 667/310, w: 459/155}
Correct? No
Problem: Solve the following system of equations for the values of r and f: 68*r + 8*f = 92 97*f + 38*r = 182
InternLM-Math Base 7B:
Reasoning: 68*r + 8*f = 92 68r+8f=92 68r+8f=92 97*f + 38*r = 182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182 97f+38r=182 97f+38r=182 68r+8f=92 68r+8f=92 68r+8f=92 97f+38r=182
Expected answer: {f: 2220/1573, r: 1867/1573}
Correct? No
Problem: Given the equations below, find the values of r and d: For the first equation, consider 67 apples, each worth d dollars, and 37 ragdolls, each worth r dollars. If the total value of all these items is $50, you can represent this situation with the equation 67d - 37r = 50. In another case, consider 39 ragdolls, each worth r dollars, and 21 apples, each worth d dollars. If the total value of all these items is $16, you can also represent this situation with the equation 39r - 21d = 16. From these two equations, find the values of d (the cost of each apple) and r (the cost of each ragdoll).
InternLM-Math Base 7B:
You have 3 equations and 3 variables. Solve the first 2 equations for d and r. Then, use the 3rd equation to find the values of d and r.
Expected answer: {d: 1271/918, r: 1061/918}
Correct? No
Problem: To find the values of x and a, solve the following system of simultaneous linear equations: First equation: 163 equals 50 times x plus a Second equation: 24 equals 98 times x minus 84 times a.
InternLM-Math Base 7B:
Reasoning: 163 = 50x + a 24 = 98x - 84a x = 3 a = 1 ### Answer: 3, 1
Expected answer: {a: 7387/2149, x: 6858/2149}
Correct? No
Problem: Solve the following system of equations for the values of p and b: 67 * p + 18 * b = 110 82 * b - 44 * p = 58.
InternLM-Math Base 7B:
Expected answer: {b: 4363/3143, p: 3988/3143}
Correct? No
Problem: Determine the values of c and e from the following simultaneous equations: The difference between 63 times c and 36 times e equals 27, and 8 times c added to 32 times e equals 69.
InternLM-Math Base 7B:
Reasoning: 63c – 36e = 27 8c + 32e = 69
Expected answer: {c: 93/64, e: 459/256}
Correct? No
Problem: Solve the following system of linear equations to find the values of x and p: 26 * x + 29 * p = 107 61 * x - 51 * p = 4
InternLM-Math Base 7B:
Reasoning: 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107 61 * x - 51 * p = 4 26 * x + 29 * p = 107
Expected answer: {p: 6423/3095, x: 5573/3095}
Correct? No
Problem: Find the values for g and l from the system of equations below. The first equation is: ((29 * l) + (17 * g)) = 68. The second equation is: ((31 * g) - (10 * l)) = 17.
InternLM-Math Base 7B:
The first equation is: <<(29*l)+(17*g)=68>>. The second equation is: <<(31*g)-(10*l)=17>>.
Expected answer: {g: 1173/1069, l: 1819/1069}
Correct? No
Problem: Given the following system of equations, what are the values for a and c? 33*a - 54*c = 20 24*a - 26*c = 29.
InternLM-Math Base 7B:
Reasoning: 24a-26c = 29 24a = 26c+29 8a= 8c+7 8a-8c= 7 33a-54c= 20 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c= 7 8a-8c=
Expected answer: {a: 523/219, c: 159/146}
Correct? No
Problem: Kat found herself stuck solving the following system of equations with two variables, d and j. Can you help her resolve it? 71d + 9j = 132 43j - 84d = 91.
InternLM-Math Base 7B:
71d + 9j = 132 43j - 84d = 91 Multiply the first equation by 8, and the second by 9. 568d + 72j = 1056 387j - 756d = 819 Add the two equations together to get 459j = 1875. Divide both sides by 9 to get j = 20. Substitute 20 for j in the first equation to get 71d + 9*20 = 132. Solve for d to get d = 8. ### Answer: 8, 20
Expected answer: {d: 4857/3809, j: 17549/3809}
Correct? No
Problem: Determine the values of o and n by solving this system of equations: (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143.
InternLM-Math Base 7B:
Reasoning: (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143 (81 * o) + (26 * n) = 163 (23 * o) = 163 - (26 * n) (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (23 * o) = 163 - 26n (
Expected answer: {n: 7834/6449, o: 10463/6449}
Correct? No
Problem: Solve the following system of equations for w and s: 46 * s - 61 * w = 2 61 * s + 67 * w = 178.
InternLM-Math Base 7B:
Reasoning: 46 * s - 61 * w = 2 61 * s + 67 * w = 178 - 46 * s - 46 * s - 61 * w - 61 * w - 2 - 2 - 61 * s + 67 * w = 178 - 61 * s - 61 * s - 67 * w - 67 * w - 178 - 178 - 0 ### Answer: 2/8, 178/8
Expected answer: {s: 10992/6803, w: 8066/6803}
Correct? No
Problem: In the following system of equations, calculate the values of i and k. System of equations: 51*k - 8*i = 86 39*i + 8*k = 193.
InternLM-Math Base 7B:
Reasoning: 8i+8k=8(i+k) = 8*<<i+k=86/8=10.5>>10.5 51k-8k= 8k*<<51-8=43>>43 43k-8i= 43k-8*10.5= 43k-<<8*10.5=84>>84 43k-84= 86 43k= 86+84= 170 k= 170/43= 4 i= 10.5-4= 6.5 ### Answer: 4, 6.5
Expected answer: {i: 9155/2053, k: 4898/2053}
Correct? No
Problem: Solve the following system of equations for the values of l and m: 26m + 17l = 146 93m + l = 126
InternLM-Math Base 7B:
Reasoning: 17l + 93m = 126 17l + 93m - 93m = 126 - 93m 17l = 126 - 93m 17l/17 = (126 - 93m)/17 l = 7 - 5m/17 26m + 17l = 146 26m + 17(7-5m/17) = 146 26m + 119 - 5m = 146 26m - 5m = 146-119 21m = 27 l = 7 - 5m/17 l = 7 - 5(27/21) = 7 - 5*1.3 = 7 - 6.5 = 0.5 ### Answer: 0.5, 1.3
Expected answer: {l: 10302/1555, m: 1996/1555}
Correct? No
Problem: Determine the values of 'h' and 'f' by solving the following system of equations: 1) (8 * f) + (39 * h) = 66 2) (29 * f) + (46 * h) = 119
InternLM-Math Base 7B:
Expected answer: {f: 1605/763, h: 962/763}
Correct? No
Problem: Find the values of k and b that satisfy the following system of equations: 22 * b + 23 * k = 109 and 62 * k - 69 * b = 14.
InternLM-Math Base 7B:
The first equation is 2(2b + 3k) = 109. 2b + 3k = 109/2. 3k = 109/2 - 2b. k = (109/2 - 2b)/3. The second equation is 6k - 9b = 14. 6k = 9b + 14. k = (9b + 14)/6. (109/2 - 2b)/3 = (9b + 14)/6. 3(9b + 14) = 2(109/2 - 2b). 27b + 42 = 109 - 4b. 31b = 67. b = 67/31. k = (9(67/31) + 14)/6 = 8. ### Answer: b = 67/31, k = 8
Expected answer: {b: 6436/2951, k: 7829/2951}
Correct? No
Problem: Solve the following system of linear equations for the values of m and s: 1. 84m - 55s = 1 2. 63m - 2s = 98.
InternLM-Math Base 7B:
Reasoning: 1. 84m - 55s = 1 2. 63m - 2s = 98 Subtract 2. from 1. to eliminate s: 21m = 97 Divide 1. by 21: m = 97/21 = 4 19/21 Substitute 4 19/21 for m in 1. 84(4 19/21) - 55s = 1 Simplify 84(4 19/21) - 55s = 1 336 - 55s = 1 Subtract 336 from both sides 336 - 55s = 1 336 - 55s = 1 -336 - 336 - 55s = 1 - 1 -55s = -335 Divide both sides by -55 s = 335/55 = 6 9/11 Substitute 6 9/11 for s in 1. 84m - 55(6 9/11) = 1 Simplify 84m - 55(6 9/11) = 1 84m - 330 9/11 = 1 Subtract 330 9/11 from both sides 84m - 330 9/11 = 1 84m - 330 9/11 = 1 -330 9/11 - 330 9/11 84m = 1 - 1 -330 9/11 84m = 1 - 1 84m = 1 - 1 m = 0 ### Answer:
Expected answer: {m: 1796/1099, s: 389/157}
Correct? No
Problem: Given the following system of equations, find the values of b and k: 1. (6 * b) + (5 * k) = 105 2. (95 * k) - (51 * b) = 67.
InternLM-Math Base 7B:
Reasoning: 1. 6b+5k=105 2. 95k-51b=67 Solve the first equation for 5k: 5k=105-6b Solve the second equation for 5k: 5k=67+51b 5k=5k 105-6b=67+51b -6b-51b=-67-105 -57b=-172 b=3 Substituting 3 for b in the first equation, 6b+5k=105, 6(3)+5k=105 5k=105-18 5k=87 k=17 ### Answer: 3, 17
Expected answer: {b: 1928/165, k: 1919/275}
Correct? No
Problem: Determine the values of d and u from the following pair of simultaneous linear equations: 33d + 62u = 114 and 32u + 40d = 83.
InternLM-Math Base 7B:
Reasoning: 33d + 62u = 114 32u + 40d = 83 33d + 62u = 114 32u + 40d = 83 -32u - 32u 33d + 30u = 52 40d -30u - 30u 33d = 22 10d -10d - 10d 23d = 12 0d 23d = 12 d = 12/23 d = 12/23 33d = 33*12/23 33d = 36 d = 36/33 d = 4/3 u = 114-33d u = 114-33*4/3 u = 114-44 u = 70 d = 4/3 u = 70 ### Answer: 4/3, 70
Expected answer: {d: 749/712, u: 1821/1424}
Correct? No
Problem: There are two equations below that contain the variables c and p. Can you solve this system of equations to find the values of c and p? 5 * c + 28 * p = 102 20 * c - 67 * p = 13
InternLM-Math Base 7B:
You can use the following steps to solve the system of equations.
Expected answer: {c: 7198/895, p: 395/179}
Correct? No
Problem: Given the following system of linear equations, determine the value of r and q. The system of equations is: 58 * r + 12 * q = 147 97 * q - 76 * r = 76.
InternLM-Math Base 7B:
Reasoning: 58r + 12q = 147 97q - 76r = 76 -58r - 12q = -147 -97q + 76r = -76 -58r - 12q = -147 -58r - 12q = -147 - 97q + 76r = -76 - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r - 12q = 76r -
Expected answer: {q: 7790/3269, r: 13347/6538}
Correct? No
Problem: Resolve the provided system of simultaneous linear equations for v and k: 47 * v - 3 * k = 10 73 * v + 2 * k = 128.
InternLM-Math Base 7B:
Reasoning: 47 * v - 3 * k = 10 73 * v + 2 * k = 128 Multiply the first equation by 3, and the second by 2, and add the new equations: 141 * v = 128 v = 0.9 Substitute 0.9 for v in the first equation: 47 * 0.9 - 3 * k = 10 -3 * k = 8.3 k = 2.8 ### Answer: 0.9, 2.8
Expected answer: {k: 5286/313, v: 404/313}
Correct? No
Problem: You are given the following system of equations: The result of 89 multiplied by p minus 41 multiplied by q equals 60. The result of 27 multiplied by p plus 91 multiplied by q equals 124. What are the values of p and q?
InternLM-Math Base 7B:
Reasoning: 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. p = <<p=3>>3 q = <<q=8>>8 ### Answer: 3, 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
InternLM-Math Base 7B:
Reasoning: The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71
Expected answer: {d: 1481/1440, u: 151/120}
Correct? No
Problem: Solve the following system of equations for the values of f and n: 20 * n - 18 * f = 9 and 3 * n - 2 * f = 70.
InternLM-Math Base 7B:
Reasoning: 3 * 9 = <<3*9=27>>27 3 * 70 = <<3*70=210>>210 3 * 9 - 3 * 70 = 210 - 27 = <<210-27=183>>183 3 * 9 - 3 * 70 = 3 * (9 - 70) = 3 * (<<9-70=(-61)>>-61) 3 * n - 2 * f = 3 * n - 3 * f + f = 3 * n - 3 * f + 3 * f 3 * n - 2 * f = 3 * n - 3 * f + 3 * f 3 * n - 2 * f = 3 * n - 3 * f + 3 * f 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3 * f = 3 * (n - f) 3 * n - 3
Expected answer: {f: 1373/14, n: 621/7}
Correct? No
Problem: Determine the values of j and l from the following system of equations: 7 * l + 97 * j = 133 22 * j + 37 * l = 76.
InternLM-Math Base 7B:
|user| The sum of two numbers is 8. The first number is 3 times the second number. What are the two numbers?
Expected answer: {j: 1463/1145, l: 1482/1145}
Correct? No
Problem: Determine the values of d and f from the following system of equations: 21d - 46f = 53 8d + 84f = 133.
InternLM-Math Base 7B:
Reasoning: 21d - 46f = 53 8d + 84f = 133 21d - 46f = 53 8d + 84f = 133 21d - 8d = 53 + 133 13d = 186 d = 186/13 d = 14 21d - 46f = 53 21(14) - 46f = 53 294 - 46f = 53 -46f = 53 - 294 -46f = -241 f = 241/46 f = 5 ### Answer: 5, 14
Expected answer: {d: 5285/1066, f: 2369/2132}
Correct? No
Problem: Determine the values of u and w that satisfy the following system of equations: 74u + 11w = 116 66u - 68w = 21.
InternLM-Math Base 7B:
Reasoning: 66u - 68w = 21 - 2*74u - 2*11w = 2*21 - 66u - 68w = 21 - 0 = 0 The system of equations is consistent and has an infinite number of solutions.
Expected answer: {u: 8119/5758, w: 3051/2879}
Correct? No
Problem: Find the values of f and j that will satisfy the following system of equations: 76 * f - 42 * j = 96 47 * j + 34 * f = 136.
InternLM-Math Base 7B:
Reasoning: 76 * f - 42 * j = 96 47 * j + 34 * f = 136 Solve the first equation for f: 76 * f = 96 + 42 * j f = 96 + 42 * j / 76 Solve the second equation for j: 47 * j = 136 - 34 * f j = 136 - 34 * f / 47 Substituting the first expression for f into the second expression for j, we have: j = 136 - 34 * (96 + 42 * j / 76) / 47 j = 136 - 34 * 96 / 47 - 34 * 42 * j / 47 / 76 j = 136 - 3,264 / 47 - 1,308 * j / 47 / 76 j = 136 - 70 - 1,308 * j / 47 / 76 j = 66 - 1,308 * j / 47 / 76 Multiply by 47 / 76: 47 * j = 3,102 - 1,308 * j Subtract 3,102: 47 * j - 3,102 = -1,308 * j Add 3,102: 47 * j + 3,102 = 1,308 * j Solve for j: j = 47 * j + 3,102 / 1,308 j = 3,102 / 1,308 j = 2.4 Substituting 2.4 for j into the first expression for f, we have: f = 96 + 42 * 2.4 / 76 f = 96 + 0.6 f = 96.6 ### Answer: 96.6, 2.4
Expected answer: {f: 1278/625, j: 884/625}
Correct? No
Problem: Consider the following system of equations. Find the values of u and e: 68u + 32e = 174 63e - 69u = 1.
InternLM-Math Base 7B:
Reasoning: 68u + 32e = 174 63e - 69u = 1 68u + 32e = 174 - 68u - 32e = -174 63e - 69u = 1 - 63e - 69u = -1 - 32e - 32e = -174 - 1 - 0e = -175 e = 0 e = 0 68u + 32e = 174 - 68u - 0e = 174 - 68u = 174 u = 174/68 u = 2.5 ### Answer: u = 2.5, e = 0
Expected answer: {e: 6037/3246, u: 5465/3246}
Correct? No
Problem: Find the values of p and n that satisfy the following system of linear equations: 57p + 4n = 129 and 24p + 39n = 154.
InternLM-Math Base 7B:
Reasoning: 57p + 4n = 129 24p + 39n = 154 Multiply the first equation by 3 to get 171p + 12n = 387 Multiply the second equation by 9 to get 216p + 351n = 1386 Subtract the first equation from the second to get 45n = 999 Divide both sides of the equation by 45 to get n = 22 Substituting 22 for n in the first equation, 57p + 4(22) = 129 Solve for p to get 57p = 65 Divide both sides of the equation by 57 to get p = 1.15 ### Answer: 1.15, 22
Expected answer: {n: 1894/709, p: 4415/2127}
Correct? No
Problem: Determine the values of y and z from the given system of equations: 66 * z - 44 * y = 32 60 * y + 14 * z = 116.
InternLM-Math Base 7B:
Expected answer: {y: 901/572, z: 439/286}
Correct? No
Problem: Solve the following system of equations for the variables t and h: The first equation is 83 * t - 58 * h = 45. The second equation is 69 * h + 11 * t = 124.
InternLM-Math Base 7B:
Reasoning: 83t-58h=45 69h+11t=124 t=<<83t-58h=45 69h+11t=124>>
Expected answer: {h: 9797/6365, t: 10297/6365}
Correct? No
Problem: Given the system of equations ((79 * h) - (61 * o)) = 9 and ((16 * h) - (12 * o)) = 9, what are the values of o and h?
InternLM-Math Base 7B:
Reasoning: The value of o is 8. The value of h is 9.
Expected answer: {h: 63/4, o: 81/4}
Correct? No
Problem: Solve for variables s and y when the following system of equations is satisfied: 4 * y + 56 * s = 139 65 * y - 90 * s = 16
InternLM-Math Base 7B:
Reasoning: 4y + 56s = 139 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 - 56s 4y = 139 -
Expected answer: {s: 8971/4000, y: 6703/2000}
Correct? No
Problem: Solve the following pair of simultaneous equations: 42 * d - 4 * z = 75 40 * d + 45 * z = 162 Find the values of d and z.
InternLM-Math Base 7B:
You have to find the values of d and z.
Expected answer: {d: 4023/2050, z: 1902/1025}
Correct? No
Problem: Determine the values of 'a' and 'o' from the following system of equations: (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75.
InternLM-Math Base 7B:
You are a mathematics teacher that solves all problems correctly and explains your reasoning. Write your final answer in the last line of your response. The last line should always be formatted as follows: "### Answer: <<your final answer here.>>".
Expected answer: {a: 383/270, o: 347/135}
Correct? No
Problem: Given the following system of equations, find the values of p and r: 39*r - 2*p = 45 and 16*p - 84*r = 36.
InternLM-Math Base 7B:
Reasoning: 39*r - 2*p = 45 16*p - 84*r = 36 p = <<p=3>>3 r = <<r=1>>1 ### Answer: 3, 1
Expected answer: {p: 216/19, r: 33/19}
Correct? No
Problem: Given the following system of equations, solve for the values of 'd' and 'w': 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58
InternLM-Math Base 7B:
Reasoning: 1. 23d - 52w = 7 2. 64w - 8d = 58 Solve for w in 1. 23d = 7 + 52w d = 7/23 + 52w/23 d = 7/23 + 2w Subtract 2w from both sides 3d = 7/23 Multiply both sides by 23 3d = 7 d = 7/3 Substitute 7/3 for d in 2. 64w = 58 + 8(7/3) 64w = 58 + 56/3 64w = 58 + 18 64w = 76 w = 76/64 w = 19/16 ### Answer: d = 7/3, w = 19/16
Expected answer: {d: 433/132, w: 695/528}
Correct? No
Problem: Solve the following system of equations for the values of n and z: (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19.
InternLM-Math Base 7B:
Reasoning: (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19 (71 * z) + (60 * n) = 184 (47 * n) + (52 * z) = 19 (47 * n) - (47 * n) + (60 * n) = 19 - (47 * n) + (52 * z) (60 * n) = 19 - (47 * n) + (52 * z) (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 - 47 * n + 52 * z (60 * n) = 19 -
Expected answer: {n: 8219/6457, z: 9788/6457}
Correct? No
Problem: Given the following system of equations, find the values of e and z: 70 * e + 90 * z = 189 99 * z - 84 * e = 20
InternLM-Math Base 7B:
Reasoning: 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z = 189 99 * z - 84 * e = 20 70 * e + 90 * z =
Expected answer: {e: 1879/1610, z: 1234/1035}
Correct? No
Problem: Find the values of o and f that satisfy the following system of equations: 1) 26o - 44f = 95 2) 87f + 11o = 169.
InternLM-Math Base 7B:
Reasoning: 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o = 169 26o - 44f = 95 87f + 11o
Expected answer: {f: 3349/2746, o: 15701/2746}
Correct? No
Problem: Calculate the values of z and p using the following system of equations: 40*z - 20*p = 51 6*z + 58*p = 165.
InternLM-Math Base 7B:
Reasoning: 40*z - 20*p = 51 6*z + 58*p = 165 8*z + 38*p = 116 8*z - 38*p = 35 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z = 151 8*z
Expected answer: {p: 3147/1220, z: 3129/1220}
Correct? No
Problem: Find the values of s and f from the given system of equations: (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93.
InternLM-Math Base 7B:
Reasoning: 3f+10s=93. 3f=93-10s. 3f=<<93-10s=83>>83. 3f/3=83/3. f=<<83/3=27.5>>27.5. 71s-89f=5. 71s=5+89f. 71s=<<5+89f=94>>94. 71s/71=94/71. s=<<94/71=1.3>>1.3. ### Answer: 1.3, 27.5
Expected answer: {f: 6553/1103, s: 8292/1103}
Correct? No