PSAT Math Grid-Ins Question 7: Answer and Explanation
Question: 7
If 3a + 2b = 37 and 7a + 4b = 85, what is the value of b2 + 6b - 10?
Correct Answer: 6
Explanation:
6
The question asks for the value of the expression b2 + 6b - 10. Solve the system of equations to find the value of b. Multiply the first equation by -2 to get -6a - 4b = -74, stack the equations, and add:
Plug in 11 for a in the original first equation to get 3(11) + 2b = 37 and then 33 + 2b = 37. Subtract 33 from both sides to get 2b = 4. Divide both sides by 2 to get b = 2. Plug b = 2 into the expression to get 22 + 6(2) - 10 = 4 + 12 - 10 = 6. The correct answer is 6.
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