Question

Mrs. Snell's math test has twenty questions and is worth 100 points. The test consists of multiple choice questions worth 3 points each and short answer questions worth 11 points each. How many multiple choice questions are on the test? Explain how you determined your solution.

Answer 1

The number of multiple-choice questions are 15.

Explanation:

Mrs. Snell's math test has twenty questions and is worth 100 points.

The test consists of multiple-choice questions and short answer questions.

Let M represents the Multiple choice questions.

Let S represents the short answer question.

It is given that the total number of question are 20.

`S+M=20` ...(1)

Also, multiple-choice questions worth 3 points each, and short answer questions worth 11 points each. The total worth of the test is 100 points.

`11S+3M=100` ...(2)

Multiply equation (1) by 3 and subtract from equation (2).

`11S+3M=100\\3S+3M=60\\\underline{-\:\:\: -\:\:\:\:\:\:\:\:-\:\:\:\:\:\:}\\8S\:\:\:\:\:\:\:\:\:\:\:\:\:=40\\S\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=5`

The total number of short answers is 5.

Put S=5 in equation 1.

`5+M=20\\M=15`

Hence, the number of multiple-choice questions are 15.