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Heather the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 5 clients who did Plan A and 6 who did Plan B. On Thursday there were 3 clients who did Plan A and 2 who did Plan B. Heather trained her Wednesday clients for a total of 7 hours and her Thursday clients for a total of 3 hours. How long does each of the workout plans last?

Respuesta :

Using a system of equations, it is found that the lengths of the workout plans are given as follows:

  • Plan A: 0.5 hours = 30 minutes.
  • Plan B: 0.75 hours = 45 minutes.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

  • Variable x: Length of a Plan A workout.
  • Variable y: Length of a Plan B workout.

From the Wednesday workouts, the following equation is built:

5x + 6y = 7.

From the Thursday workouts, the following equation is built:

3x + 2y = 3.

Hence the system is:

  • 5x + 6y = 7.
  • 3x + 2y = 3.

We can multiply the second equation by -3 and add them, hence:

  • 5x + 6y = 7.
  • -9x - 6y = -9.

-4x = -2

4x = 2

x = 0.5 hours = 30 minutes.

2y = 3 - 3x

2y = 1.5

y = 1.5/2

y = 0.75 hours = 45 minutes.

Hence the lengths of the workout plans are given as follows:

  • Plan A: 0.5 hours = 30 minutes.
  • Plan B: 0.75 hours = 45 minutes.

More can be learned about a system of equations at https://brainly.com/question/24342899

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