Question

What are the important variables in the problem below?

A test is worth 60 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 5 points. If the test has 15 questions, how
many multiple-choice questions are there?
O
A. for test, q for questions
O
B. m for multiple choice, sfor short answer
O
c. p for points, m for multiple choice
O
D. sfor short answer, t for test

Answer 1

The important variables in the problem are:

B.
`m` for multiple choice,
`s` for short answer

The number of multiple choice questions = 5

Explanation:

Given:

Total number of questions = 15

Total points for the test = 60

Multiple choice question carries = 2 points

Short-answer question carries = 5 points

To determine the number of multiple choice questions in the test.

Solution:

Let
`m` represent the number of multiple choice questions.

If 1 multiple choice question carries = 2 points

The,
`m` questions will carry =
`2m` points

Let
`s` represent the number of short-answer questions.

If 1 short-answe question carries = 5 points

The,
`s` questions will carry =
`5s` points

Total questions can be given as :

`m+s`

Total points can be given as :

`2m+5s`

Thus, we can model two equations form the given data.

A)
`m+s=15` [Number of questions]

B)
`2m+5s=60` [ Total points]

Thus,
`m` and
`s` are important variables in the problem.

Rearranging equation A, to solve for
`s` in terms of
`m`

Subtracting both sides by
`m`

`m+s-m=15-m`

`s=15-m`

Substituting value of
`s` we got from A into equation B.

`2m+5(15-m)=60`

Using distribution.

`2m+75-5m=60`

Simplifying.

`-3m+75=60`

Subtracting both sides by 75.

`-3m+75-75=60-75`

`-3m=-15`

Dividing both sides by -3.

`(-3m)/(-3)=(-15)/(-3)`

∴
`m=5`

Thus, number of multiple choice questions = 5