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 = 153m + 5f = 51How many multiple-choice questions are on the test?
The test has 15 questions, so m + f = 15. Substitute m = 15 − f into the time equation: 3(15 − f) + 5f = 51, which gives f = 3 and m = 12. Therefore, the test has 12 multiple-choice questions, choice C.
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