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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

User Farrokh
by
8.6k points

1 Answer

1 vote

Answer:

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

User Jahn
by
7.1k points

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