Solving a word problem using a system of linear equations of the form Ax + By = C

Question

Ravi 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 2 clients who did Plan A and 5 who did Plan B. On Saturday there were 8 clients who did Plan A and 3 who did Plan B. Ravi trained his Friday clients for a total of 8 hours and his Saturday clients for a total of 15 hours. How long does each of the workout plans last?

Answer 1

2a + 5b = 8

8a + 3b = 15

We see that if we multiply the 1st equation by -4, we can cancel out the a.

-8a - 20b = -32

8a + 3b = 15

Adding the equations together...

-17b = -17

b = 1 hour

2a + 5(1) = 8

2a + 5 = 8

2a = 3

a = 3/2 = 1 1/2 hours