Algebra Linear Equation?

Question

Laura 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 Wednesday there were 9 clients who did Plan A and 7 who did Plan B. On Thursday there were 3 clients who did Plan A and 5 who did Plan B. Laura trained her Wednesday clients for a total of 12 hours and her Thursday clients for a total of 6 hours. How long does each of the workout plans last?

Length of each Plan A workout:

Length of each Plan B workout: 

Answer 1

Laura 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 Wednesday there were 9 clients who did Plan A and 7 who did Plan B. 

On Thursday there were 3 clients who did Plan A and 5 who did Plan B. 

Laura trained her Wednesday clients for a total of 12 hours 

and her Thursday clients for a total of 6 hours. 

How long does each of the workout plans last?

Create a system of equations 

let A be the duration of a Plan A session and B be the duration of a Plan B session

For Wednesday: 9A + 7B = 12 hours

For Thursday: 3A + 5B = 6 hours

Multiply the Thursday equation by 3 then solve the system through subtraction:

9A + 7B = 12

(3A + 5B = 6) * 3

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

8B = 6

 

B = 0.75 hours

plug that into one of the original equations:

3A + 5(0.75) = 6

3A = 2.25

A = 0.75

 

Length of each Plan A workout: 0.75 hours

Length of each Plan B workout: 0.75 hours