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.
Let y be the number of strength-training exercises per week. Let x be the number of aerobic exercises per week. For the beginner plan: 15y + 20x = 90 ..........(1) For the advanced plan: 20y + 30x = 130 ........(2) Multiply both sides of (1) by 3 to get: 45y + 60x = 270 ........(3) Multiply both sides of (2) by2 to get: 40y + 60x = 260 .......(4) Subtracting (4) from (3) we get: 5y = 10 y = 2 Plugging in the value of 2 for y in equation and solving, we find x = 3. Therefore the correct statement is: "Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week."
