solving a word problem using a system of linear equatations

Question

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

length of plan a

length of plan b

Answer 1

Hi James,

Let A = number of hours that workout plan A lasts.

B = number of hours that workout plan B lasts.

The problem gives us two equations:

3A + 2B = 4 (the Friday clients did a total of 4 hours)

8A + 4B = 9 (the Saturday clients did a total of 9 hours)

If we multiply the entire top equation by -2 we get:

-6A - 4B = -8

8A + 4B = 9

Now if we add the two equations together we get:

2A = 1 (the B’s cancel out due to their opposite sign)

A = 0.5 hours.

We can replace A with 0.5 in the second equation:

8(0.5) + 4B = 9

4 + 4B = 9

4B = 5

B = 1.25 hours.

Please let me know if I can be more helpful, thanks!

Joe