Math assistance needed please.

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

Answer 1

3A+5B=6

9A+7B=12 is the system of equations you would use to solve this problem.

Ans: Plan A=3/4 Plan B=3/4 What is 3/4 of an hour?

Answer 2

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

>> Ann trained her Monday clients for a total of 6 hours

3*A+5*B = 6

>> On Tuesday there were 9 clients who did Plan A and 7 who did Plan B.

>> Ann trained her Tuesday clients for a total of 12 hours.

9*A+7*B = 12

Step 1:

3*A + 5*B = 6 (Multiply both sides with 3 to get 9*A in the equation)

9*A + 7*B = 12

Step 2:

9*A + 15*B = 18 (Subtract second equation from the firs one -> 9*A-9*A = 0, 15*B-7*B = 8*B, 18-12 = 6)

9*A + 7*B = 12

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

0 + 8*B = 6

Step 3:

B = 6/8 = 3/4 (Divide both sides by 8)

Step 4: Substitute B in the first equation with B=3/4

3*A + 5*3/4 = 6

3*A + 15/4 = 6 (subtract 15/4 from both sides)

3*A = 6 - 15/4 (Divide both sides by 3)

A = 2 - 5/4

A = 2/1 - 5/4

A = 8/4 - 5/4

A = 3/4