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Deshaun the trainer has two solo workout plans that he offers his 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 5 who did Plan B. On Tuesday there were 6 clients who did Plan A and 2 who did Plan B. Deshaun trained his Monday clients for a total of 10 hours and his Tuesday clients for a total of 10 hours. How long does each of the workout plans last?

Answer :

Answer:

Plan A and plan B both lasts for 1.25 hours.

Step-by-step explanation:

Trainer has two solo workout plans Plan A and Plan B.

Let the trainer trains for plan A = x hours and for plan B = y hours

As per statement given in the question,

"Dueshan trained his Monday clients for a total of 10 hours"

Equation will be, 3x + 5y = 10 --------(1)

And other statement says,

"Dueshan trained his Tuesday clients for a total of 10 hours"

6x + 2y = 10

3x + y = 5

y = 5 - 3x ----------(2)

Replace the value of y in equation 2 from equation 1.

3x + 5(5 - 3x) = 10

3x + 25 - 15x = 10

25 - 12x = 10

12x = 25 - 10

12x = 15

x = [tex]\frac{15}{12}[/tex]

x = 1.25 hours

From equation 1

y = 5 - 3×1.25

y = 5 - 3.75

y = 1.25 hours

Therefore, plan A and plan B both lasts for 1.25 hours.

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