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

Determine equations that represent each condition;

Fri.; 5A + 3B = 12, Sat., 2A + 12B = 21

Apply a factor to ONE or BOTH equations that will help you isolate ONE of the terms (A or B) so you can solve for the left over term.

Here I will factor the Friday equation by -4 so we modify the B term so when we add the two equations, the B term cancels out...

-4(5A + 3B) = 12(-4); -20A -12B = -48

Add the two equations;

-20A - 12B = -48

2A + 12B = 21 ....The B term cancels out

(-20A + 2A) = (-48 + 21)

-18A = -27 ... divide by -18 to isolate A and reduce fraction

A = -27/-18 = 27/18 = 3/2 = 1 1/2 (hrs)

A = 1 1/2 (hrs)

Plug in A value into one of the two equations and solve for B;

B = [12 - 5(1.5)]/3 = (12 - 7.5)/3 = 4.5/3 = 1.5(hrs.)

B= 1 1/2 (hrs)

If you plug in the values of A & B into the 2nd equation, you will see that the values make the statement true.