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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.

User Coinbird
by
8.4k points

2 Answers

10 votes

Final answer:

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.

8 votes

Answer:

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.

User Milan Kamilya
by
7.5k points

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