Question

tudents are given 3 minutes for each multiple-choice question and 5 minutes for each free-response question on a test. There are 15 questions on the test, and students are given 51 minutes to take it. The system of equations shown can be used to find the number of multiple-choice questions, m, and the number of free-response questions, f, on the test. m + f = 15 3m + 5f = 51 How many multiple-choice questions are on the test? 3 5 12 14

Answer 1

In this question, they gave you the system of equations. You just need to use the two of them.

We want to find the m or the number of the multiple-choice questions. So we need to turn our last equation in the form of 'm's by translating the 'f's into 'm's.

$m + f = 15$
$f = 15 - m$

If we know the m form of f, we can convert the second equation and find the answer: $3m + 5f = 51$

Plug in the m value of f: $3m + 5(15 - m) = 51$

Distribute the 5: $3m + 75 - 5m = 51$

Subtract -75 from both sides: $3m - 5m= 51 - 75$

Combine like terms: $- 2m = - 24$

Divide both sides by -2: $m = 12$

So, we learned that the number of the multiple-choice questions is 12.