Melissa 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 3 clients who did Plan A and 2 who did Plan B. On Tuesday there were 5 clients who did Plan A and 6 who did Plan B. Melissa trained her Monday clients for a total of 3 hours and her Tuesday clients for a total of 7 hours. How long does each of the workout plans last?

Question

Mathematics

Alannah Gilmore

1 June, 12:14

Melissa 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 3 clients who did Plan A and 2 who did Plan B. On Tuesday there were 5 clients who did Plan A and 6 who did Plan B. Melissa trained her Monday clients for a total of 3 hours and her Tuesday clients for a total of 7 hours. How long does each of the workout plans last?

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Answers (1)

Know the Answer?

Nathan · Answer 1

Answer: Plan A lasts for 30 minutes and Plan B lasts for 45 minutes.

Step-by-step explanation:

Let's consider plan A is x, and Plan B is y. For Monday, according to the conditions, the equation will be 3x + 2y = 3, and for Tuesday, the equation will be 5x+6y = 7. Now, multiplying the first equation with five and second equation with three we get, 15x+10y = 15 and 15x + 18y = 21. Subtracting these two equations, we get, 8y = 6

Or y = 3/4. Putting the value of in any equation, we get the value of x, which is 1/2.

1/2 hours means 30 minutes and 3/4 hours means 45 minutes. Thus Plan A is 30 minutes and Plan B is 45 minutes.