Question

What are the important variables in the problem below?

Answer 1

Answer:

The important variables in the problem are:

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

The number of multiple choice questions = 5

Step-by-step 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.

$\frac{-3m}{-3}=\frac{-15}{-3}$

∴ $m=5$

Thus, number of multiple choice questions = 5