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The trainer has 2 solo workout plans, Plan A and Plan B that he offers his clients. Plan A and Plan B each client does 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 did Plan B. He trained his clients for a total of 9 hours on Friday and his clients on Saturday for a total of 4 hours. How long does each workout plan last?

User Vcardillo
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1 Answer

6 votes

Let's define the next variables:

x: duration of plan A, in hours

y: duration of plan B, in hours

On Friday there were 4 clients who did Plan A and 8 who did Plan B, and the total time of training was 9 hours, then:

4x + 8y = 9 (eq. 1)

On Saturday there were 2 clients who did Plan A and 3 did Plan B, and the total time of training was 4 hours, then:

2x + 3y = 4 (eq. 2)

Multiplying equation 2 by 2, we get:

2(2x + 3y) = 2*4

2*2x + 2*3y = 8

4x + 6y = 8 (eq. 3)

Subtracting equation 3 to equation 1:

4x + 8y = 9

-

4x + 6y = 8

-------------------

2y = 1

y = 1/2

Substituting this result into equation 1 and solving for x:

4x + 8*1/2 = 9

4x + 4 = 9

4x = 9 - 4

4x = 5

x = 5/4

In conclusion, plan A lasts 5/4 hours, and plan B lasts 1/2 hours

User NawaMan
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