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.

Respuesta :

Answer:

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

A total of 16 questions.

Step-by-step explanation:

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

Let it be equal to [tex]x[/tex]

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

→Total time it takes to attempt multiple choice question = [tex]2 * x[/tex] minutes

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

→Total Time it takes to attempt short answer type question = [tex]3.5 * x[/tex] 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:

[tex]2x +3.5x <45[/tex]

[tex]\\ 5.5x <45[/tex]

[tex]x < 8.18[/tex]

Hence the value of [tex]x = 8[/tex]