Question

Keiko 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 2 clients who did Plan A and
12 who did Plan B. Keiko trained her Monday clients for a total of 7 hours and her Tuesday clients for a total of 19 hours. How long
does each of the workout plans last?

Answer 1

• Plan A: 0.5 hours
• Plan B: 1.5 hours

Explanation:

You want to know the time each of workouts A and B last if their combinations are ...

• 5A + 3B = 7 hours
• 2A + 12B = 19 hours

Solution

Subtracting the second equation from 4 times the first gives ...

4(5A +3B) -(2A +12B) = 4(7) -(19)

18A = 9 . . . . . . . . . simplify

A = 9/18 = 1/2

Using the second equation to find B, we have ...

2(1/2) +12B = 19

12B = 18

B = 18/12 = 3/2

Workout plan A lasts 1/2 hour; plan B lasts 1 1/2 hours.

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