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

Answer 1

From m + f = 15, m = 15 − f. Substitute into 3m + 5f = 51:

3(15 − f) + 5f = 51
45 − 3f + 5f = 51
2f = 6
f = 3

Then m = 15 − 3 = 12.

So there are 12 multiple-choice and 3 free-response questions.