Question

select the correct answer from each drop - down menu.
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.

Explanation:

Step1: Define variables and time per question

Let \( n \) be the number of multiple - choice questions (and also the number of short - answer questions, since they are equal in number). The time to complete each multiple - choice question is 2 minutes, so the total time for multiple - choice questions is \( 2n \) minutes. The time to complete each short - answer question is 3.5 minutes, so the total time for short - answer questions is \( 3.5n \) minutes.

Step2: Set up the inequality

The total time to complete the test is the sum of the time for multiple - choice and short - answer questions, and this total time must be less than 45 minutes. So the inequality is \( 2n+3.5n < 45 \).

Step3: Combine like terms

Combine the terms with \( n \): \( (2 + 3.5)n<45 \), which simplifies to \( 5.5n < 45 \).

Answer:

The inequality is \( 2n + 3.5n<45 \) (or \( 5.5n < 45 \))