Solving Systems of Linear Equations: Linear Combinations
Question 5 • TX-Algebra I A-CR
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.
Answer
A
Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.
B
Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
C
Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.
D
Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.
Explanation
Let s be the number of strength-training sessions and a the number of aerobic sessions per week. The beginner plan gives 15s + 20a = 90, and the advanced plan gives 20s + 30a = 130. Solving these equations gives s = 2 and a = 3, so each plan uses 2 strength-training sessions and 3 aerobic exercise sessions per week.
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