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

Question

Kira 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 Friday there were 5 clients who did Plan A and 3 who did Plan B. On Saturday there were 2 clients who did Plan A and 12

who did Plan B. Kira trained her Friday clients for a total of 12

hours and her Saturday clients for a total of 21 hours.

How long does each of the workout plans last?

Workout plan A:

Workout plan B:

Answer 1

We know that the total amount of time on Friday was 12 hours. Since 5 clients used plan A and 3 used plan B on Friday, we could say 5A + 3B = 12, where A and B represent the durations of each plan. Using the same strategy for Saturday, we could say 2A + 12B = 21. This is the system of equations you should use to solve this problem.