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

Question

Rita 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 3 clients who did Plan A and 5 who did Plan B. On Thursday there were 12 clients who did Plan A and 2 who did Plan B. Rita trained her Wednesday clients for a total of 12 hours and her Thursday clients for a total of 21 hours.

How long does each of the workout plans last?

Answer 1

two simultaneous equations in two unknowns A and B, the length of two classes in hours

(1) 3A + 5B = 12

(2) 12A + 2B = 21

4 x (1) - (2) to eliminate A

12A + 20B = 48

-

12A + 2B = 21

=

0A + 18B = 27

=> B = 27/18 = 1.5

substitute value of B in (1) to get 3(1.5) + 5B = 12

=> 5B = 12 - 4.5 = 7.5

=> B = 1.5

Hence Class A = Class B = 90 minutes (or 1.5 hours)

Double-check? 3(1.5) + 5(1.5) = 4.5 + 7.5 = 12 and 12(1.5) + 2(1.5) = 18 + 3 = 21 both as required.