Question

Students 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?

Answer 1

You need to solve for m, either by elimination or substitution.

In this case, I'd personally substitution by converting m+f=15 to f=15-m. Plug and chug into the second equation and you'll get m.