Math Linear Equations, Finding two variables

Question

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?

Answer 1

Let's look at this problem as two separate parts.

Part 1: number of questions

Part 2: number of points

Part 1:

We know that there are 20 questions total. These questions are made up of T/F and multiple choice questions. To represent T/F, lets use x. To represent MC, let's use y.

x = number of T/F

y = number of MC

x + y = 20

Part 2: The total amount of points is 100. T/F questions are worth 3 points, and MC questions are worth 11 points. Since x represents the number of T/F questions, we multiply 3 and x to get the points earned on T/F questions. We also multiply 11 and y for MC.

3x + 11y = 100

Our system is as follows:

x + y = 20

3x + 11y = 100

You may solve this any way you would like. I will show substitution below:

The first equation can be rearranged by subtracting y from both sides. You get x = 20 - y. Let's substitute 20 - y in for x in the second equation.

3 (20 - y) + 11y = 100

Distribute 3 to 20 and -y

60 - 3y + 11y = 100

Combine -3 and 11y

60 + 8y = 100

Subtract 60 from both sides

8y = 40

Divide both sides by 8

y = 5

This means that there were 5 Multiple Choice questions on the test.