Question

A history teacher is writing a test worth 100 points. She uses multiple-choice questions worth 6 points each and true/false questions worth 2 points each. She wants the test to have three times as many multiple-choice questions as true/false questions. Let m represent the number of multiple-choice questions on the test and let t represent the number of true/false questions. Which system of equations can be used to find how many of each type of question she should write? (A)6m + 2t = 100, t=3m (B)3m +t = 100, m=3t (C) 6m + 2t = 100 m = 3t (D) 6m + 2t = 100, m= t + 3

Answer 1

(C)6m+2t=100, m=3t

Step-by-step explanation:

Given the following:

• The number of multiple-choice questions on the test = m

,

• The number of true/false questions = t

Each multiple-choice is worth 6 points, and;

Each true/false question worth 2 points.

The test is worth 100 points, therefore, we have that:

`6m+2t=100`

Also, the teacher wants the test to have three times as many multiple-choice questions as true/false questions.

This means that:

`m=3t`

Therefore, the system of equations can be used to find how many of each type of question she should write is:

6m+2t=100

m=3t

The correct choice is C.