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.How many multiple-choice questions are on the test?

Answer 1

There are 12 multiple choice

Explanation:

Let m = multiple choice

f = free response

f+m = 15 since there are 15 questions

3m+5f = 51 since we have 51 minutes and 3 for multiple choice and 5 for free response

We have 2 equations and 2 unknowns

m+f = 15

3m+5f = 51

Multiply the first equation by -3

-3(m+f) = -3*15

-3m -3f = -45

Add this to the second equation

-3m-3f = -45

3m+5f = 51

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2f = 6

Divide by 2

2f/2 = 6/2

f = 3

There are 3 free response.

m+f = 15

m+3 = 15

Subtract 3 from each side

m+3-3=15-3

m=12

There are 12 multiple choice