Question

Aldo the trainer has two solo workout plans that he offers his clients: plan a and plan b. Each client does either one or the other (not both). On friday there 8 were clients who did plan a and 3 who did plan b. On saturday there were 3 clients who did plan a and 5 who did plan b. Aldo trained his friday clients for a total of 7 hours and his saturday clients for a total of 6 hours. How long does each of the workout plans last?

Answer 1

x = number of hours to train plan a clients

x = 0.55 hour

y = number of hours to train plan b clients

y = 0.87 hours

Explanation:

Friday

Plan a = 8 clients

Plan b = 3 clients

Total hours = 7

Saturday

Plan a = 3 clients

Plan b = 5 clients

Total hours = 6

Let

x = number of hours to train plan a clients

y = number of hours to train plan b clients

8x + 3y = 7 (1)

3x + 5y = 6 (2)

Multiply (1) by 5 and (2) by (3)

40x + 15y = 35 (3)

9x + 15y = 18 (4)

Subtract (4) from (3)

40x - 9x = 35 - 18

31x = 17

Divide both sides by 31

x = 17 / 31

= 0.548 hour

Approximately

x = 0.55 hour

Substitute x = 0.55 hour into (1)

8x + 3y = 7

8(.55) + 3y = 7

4.4 + 3y = 7

3y = 7 - 4.4

3y = 2.6

Divide both sides by 3

y = 2.6 / 3

= 0.867 hours

Approximately

y = 0.87 hours

x = number of hours to train plan a clients

x = 0.55 hour

y = number of hours to train plan b clients

y = 0.87 hours