Question

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

Answer 1

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:

$5x + 3y = 6$

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

$7x + 9y = 12$

The system is:

$5x + 3y = 6$

$7x + 9y = 12$

Multiplying the first equation by -3:

$-15x - 9y = -18$

$7x + 9y = 12$

Adding them:

$-8x = -6$

$8x = 6$

$x = \frac{3}{4}$

In minutes, x = 45 minutes.

Then:

$9y = 12 - 7x$

$9y = 12 - 7(0.75)$

$y = \frac{12 - 7(0.75)}{9}$

$y = 0.75$

Also 45 minutes.

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