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 total time for questions

Let \( n \) be the number of multiple - choice questions (and also the number of short - answer questions). The time for multiple - choice questions: each takes 2 minutes, so for \( n \) questions, time is \( 2n \) minutes. The time for short - answer questions: each takes 3.5 minutes, so for \( n \) questions, time is \( 3.5n \) minutes. The total time \( T=2n + 3.5n\).

Step2: Simplify the total time expression

Combine like terms: \( 2n+3.5n=(2 + 3.5)n=5.5n \) minutes.

Step3: Set up the inequality

The test must take less than 45 minutes, so \( 5.5n<45 \).

Answer:

The inequality is \( 5.5n < 45 \)