Final answer:
The teacher can include a maximum of 8 multiple-choice questions and 8 short answer questions in the test to ensure it takes students less than 45 minutes to complete.
Step-by-step explanation:
To determine how many questions the teacher can include in the test, we need to consider the time it takes to complete each type of question.
Let's assume there are x multiple-choice questions and x short answer questions. The time it takes to complete the multiple-choice questions is 2 minutes per question, so the total time for multiple-choice questions is 2x minutes.
Similarly, the time it takes to complete the short answer questions is 3.5 minutes per question, so the total time for short answer questions is 3.5x minutes. The total time for the whole test should be less than 45 minutes, so we can set up the inequality:
2x + 3.5x < 45
5.5x < 45
x < 45/5.5
x < 8.18
Since we can't have a fraction of a question, the teacher can include a maximum of 8 multiple-choice questions and 8 short answer questions in the test to ensure it takes students less than 45 minutes to complete.