Question

Max and Sasha exercise a total of 20 hours each week. Max exercises 15 hours less than 4 times the

number of hours Sasha exercises. The system of equations shown below represents this situation, where

x represents the number of hours Max exercises and y represents the number of hours Sasha exercises.

How many hours do Max and Sasha exercise per week?

(x + y = 20

x - 4y =-15

Max exercises

hours a week and Sasha exercises

hours a week.

Answer 1

Using the elimination method, Max exercises 13 hours per week and Sasha exercises 7 hours per week.

Step-by-step explanation:

To solve the system of equations given by:

• x + y = 20
• x - 4y = -15

We can use the substitution or elimination method. Here, we will use the elimination method.

Multiply the first equation by 4:

• (4)(x + y) = (4)(20)
• 4x + 4y = 80

Now, we have a new system of equations:

• 4x + 4y = 80
• x - 4y = -15

Add these two equations to eliminate the y variable:

• (4x + 4y) + (x - 4y) = 80 - 15
• 4x + x = 65
• 5x = 65

Divide both sides by 5 to solve for x:

• x = 65 / 5
• x = 13

Now, substitute x = 13 into the first original equation to solve for y:

• 13 + y = 20
• y = 20 - 13
• y = 7

Max exercises 13 hours a week and Sasha exercises 7 hours a week.

Answer 2

Max exercises 13 hours a week, and Sasha 7.

Step-by-step explanation:

To find the number of hours each of them exercises during the week, we solve the system of equations.

In the second equation:

`x = 4y - 15`

Replacing in the first equation:

`x + y = 20`

`4y - 15 + y = 20`

`5y = 35`

`y = (35)/(5)`

`y = 7`

So Sasha exercises 7 hours per week.

Max:

`x + y = 20`

`x + 7 = 20`

`x = 13`

Max exercises 13 hours a week.