Question

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and the short response question are worth 8 points each. Write a linear system that represents this situation. How many multiple choice and short response questions are on the test?

Answer 1

Answer: the number of multiple choice questions in the test is 12.

the number of short response questions in the test is 8.

Explanation:

Let x represent the number of multiple choice questions in the test.

Let y represent the number of short response questions in the test.

The total number of questions in the test is 20. It means that

x + y = 20

The multiple choice questions are worth 3 points each and the short response question are worth 8 points each. The total number of points is 100. It means that

3x + 8y = 100 - - - - - - - - - - 1

Substituting x = 20 - y into equation 1, it becomes

3(20 - y) + 8y = 100

60 - 3y + 8y = 100

- 3y + 8y = 100 - 60

5y = 40

y = 40/5 = 8

x = 20 - y = 20 - 8

x = 12