Answer:
Step-by-step explanation:
Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
Step-by-step explanation:
Let x represent the number of strength-training sessions and y represent the number of aerobic sessions per week.
For the beginner plan, we have
15x+20y = 90. This is because 15 minutes of strength training (x) and 20 minutes of aerobic exercise (y) gives 90 minutes of exercise.
For the advanced plan, we have
20x+30y = 130. This is because 20 minutes of strength training (x) and 30 minutes of aerobic exercise (y) gives 130 minutes of exercise.
This gives us the system
To solve this, we will make the coefficients of y the same. To do this, we multiply the top equation by 3 and the bottom equation by 2:
Now to eliminate the y terms, we subtract the second equation from the first:
Divide both sides by 5:
5x/5 = 10/5
x = 2
Substitute this in the first equation:
15(2)+20y=90
30+20y = 90
Subtract 30 from each side:
30+20y-30 = 90-30
20y = 60
Divide both sides by 20:
20y/20 = 60/20
y = 3
Each plan uses 2 strength training sessions (x) and 3 aerobic sessions (y) each week.
