Ann 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).

Question

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

Answer 1

7a + 9b = 12

5a + 3b = 6

-Solve this system of equations by multiplying both sides of one of the equation so that when the equations are added or subtracted there will only be one variable.

-I will multiply both sides of the 2nd equation by -3

-3*(5a + 3b) = 6*-3

-15a - 9b = -18

-Now I will get rid of the variable b by adding the two equations together.

7a + 9b = 12

+ -15a - 9b = -18

-8a = -6

a = -6/-8

a= 3/4 (45 minutes)

-Now plug 3/4 into one of the original equations as a to solve for b.

-I will use the 2nd original equation.

5a + 3b = 6

5(3/4) + 3b = 6

15/4 + 3b = 6

3b = 9/4

b = 9/12 = 3/4 (45 minutes)

Both workout plans last the same amount of time.

Plan A lasts 45 minutes.

Plan B lasts 45 minutes.