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 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." 

Answer 2

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

Step-by-step explanation: