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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.

Respuesta :

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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." 

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

How to Solve Algebra Word Problems?

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, the equation would be gotten as;

15y + 20x = 90  ------(eq 1)

The equation to represent the advanced plan would be;

20y + 30x = 130   -------(eq 2)

Multiply both sides of eq 1 by 4 to get:

60y + 80x = 360 ------(eq 3)

Multiply both sides of eq 2 by 3 to get:

60y + 90x = 390   ------(eq 4)

Subtract  eq(3) from eq(4) we get:

10x = 30

Thus; x = 3

Then; 15y + 20(3) = 90

15y = 30

y = 2

Thus, the correct statement is:

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

Read more about Algebra Word Problems at; https://brainly.com/question/4344214

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