Question

A teacher is making a history test composed of the same number of multiple-choice questions as short-answer questions. She estimates it will take students an average of 2 minutes to complete each multiple-choice question and an average of 3.5 minutes to complete each short-answer question.

Write an inequality to determine how many questions, n, the teacher can include if the test must take students less than 45 minutes to complete.

Answer 1

8 questions each for short answer questions and 8 questions of Multiple Choice Questions type.

A total of 16 questions.

Explanation:

The number of multiple-choice questions and the number of short answer type questions are the same.

Let it be equal to
`x`

→Average time it takes to attempt multiple choice question = 2 minutes

→Total time it takes to attempt multiple choice question =
`2 * x` minutes

→Average time it takes to attempt short answer type question = 3.5 minutes

→Total Time it takes to attempt short answer type question =
`3.5 * x` minutes

Total time for the test should be less than 45 minutes.

Now finally, we can make an equation out of the information listed above:

`2x +3.5x <45`

`\\ 5.5x <45`

`x < 8.18`

Hence the value of
`x = 8`