Question

A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has 15 minutes per session of strength-training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength-training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week.

Which statement describes when the plans are based on the same number of aerobic exercise sessions?

Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.
Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.
Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.

Answer 1

Let s = number of strength sessions and a = number of aerobic sessions per week. Then

15s + 20a = 90
20s + 30a = 130.

Subtracting (first) from (second) gives 5s + 10a = 40 → s + 2a = 8. From the first, 15s + 20a = 90 → divide by 5: 3s + 4a = 18. Solve the system (or substitute s = 5 − a from earlier work): you get a = 3 and s = 2.

So each plan uses 2 strength sessions and 3 aerobic sessions per week.