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ammy 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 Monday there were 5 clients who did Plan A and 3 who did Plan B. On Tuesday there were 7 clients who did Plan A and 9 who did Plan B. Tammy trained her Monday clients for a total of 6 hours and her Tuesday clients for a total of 12 hours. How long does each of the workout plans last

Sagot :

Using a system of equations, it is found that both workout plans last 45 minutes.

For the system, we have that:

  • x is the length of a Plan A workout.
  • y is the length of a Plan B workout.

On Monday there were 5 clients who did Plan A and 3 who did Plan B, for a total of 6 hours, hence:

[tex]5x + 3y = 6[/tex]

On Tuesday there were 7 clients who did Plan A and 9 who did Plan B, for a total of 12 hours, hence:

[tex]7x + 9y = 12[/tex]

The system is:

[tex]5x + 3y = 6[/tex]

[tex]7x + 9y = 12[/tex]

Multiplying the first equation by -3:

[tex]-15x - 9y = -18[/tex]

[tex]7x + 9y = 12[/tex]

Adding them:

[tex]-8x = -6[/tex]

[tex]8x = 6[/tex]

[tex]x = \frac{3}{4}[/tex]

In minutes, x = 45 minutes.

Then:

[tex]9y = 12 - 7x[/tex]

[tex]9y = 12 - 7(0.75)[/tex]

[tex]y = \frac{12 - 7(0.75)}{9}[/tex]

[tex]y = 0.75[/tex]

Also 45 minutes.

A similar problem, also solved using a system of equations, is given at https://brainly.com/question/14183076