Question

A test consists of 20questions. Multiple choice questions earn 4points for a correct answer, and free response questions earn 8points for a correct answer. If the test is out of 100points, how many of each type of question are on the test?

Answer 1

Answer:

15 multiple choice questions

5 free response questions

Step-by-step explanation:

This is basically a systems of equations word problem.

To solve this, we need to create two equations that represent this scenario. Let's suppose $m$ represents the amount of multiple choice questions and $f$ represents the amount of free-choice questions.

We can create the following equations:

$4m + 8f = 100$

$m+f=20$

To solve for m and f, we can use elimination.

Let's multiply the equation $m+f=20$ by -4.

$-4m - 4f = -80$

Great! Now let's add this equation to our first one, $4m + 8f = 100$.

$4m + 8f = 100$

$-4m - 4f = -80$

___________________

$0m + 4f = 20$

$4f=20$

Dividing both sides by 4 get us $f=5$.

So there are 5 free choice questions. To find m, we can substitute inside the equation $m+f=20$

$m+5=20\\\\m=20-5\\\\m=15$

So there are 15 multiple choice questions.

Hope this helped!