Question

Elsa 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 Friday there were 4 clients who did Plan A and 8 who did Plan B. On Saturday there were 2 clients who did Plan A and 3 who did Plan B. Elsa trained her Friday clients for a total of 9 hours and her Saturday clients for a total of 4 hours. How long does each of the workout plans last?

Answer 1

Answer: plan A lasts for 1.25 hours.

Plan B lasts for 0.5 hour.

Step-by-step explanation:

Let x represent the number of hours that plan A lasts.

Let y represent the number of hours that plan B lasts.

On Friday there were 4 clients who did Plan A and 8 who did Plan B. Elsa trained her Friday clients for a total of 9 hours. This means that

4x + 8y = 9 - - - - - - - - - - - - -1

On Saturday there were 2 clients who did Plan A and 3 who did Plan B. Elsa trained her Saturday clients for a total of 4 hours. This means that

2x + 3y = 4 - - - - - - - - - - - 2

Multiplying equation 1 by 1 and equation 2 by 2, it becomes

4x + 8y = 9

4x + 6y = 8

Subtracting, it becomes

2y = 1

y = 1/2 = 0.5

Substituting y = 0.5 into equation 1, it becomes

4x + 8 × 0.5 = 9

4x + 4 = 9

4x = 9 - 4 = 5

x = 5/4

x = 1.25