Question

Ahmad 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 Monday there were clients 3 who did Plan A and 2 who did Plan B. On Tuesday there were 5 clients who did Plan A and 6 who did Plan B. Ahmad trained his Monday clients for a total of 3 hours and his Tuesday clients for a total of 7 hours. How long does each of the workout plans last? please help

Answer 1

Plan A last for 30 minutes

Plan B last for 45 minutes

Explanation:

There are two plans:

Plan A

Plan B

Monday

Plan A=3 clients

Plan B=2 clients

Total hours=3

Tuesday

Plan A=5 clients

Plan B=6 clients

Total hours=7

The equation for the unknown

3A + 2B=3 (1)

5A + 6B=7 (2)

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

9A + 6B=9 (3)

5A + 6B=7 (4)

Subtract (4) from (3)

4A=2

Divide both sides by 4

4A/4 = 2/4

A=1/2 hours

Substitute A=1/2 into (1)

3A + 2B=3

3(1/2) +2B=3

3/2 + 2B=3

2B= 3 - 3/2

2B= 6-3/2

2B=3/2

Divide both sides by 2

B=3/2÷2

=3/2×1/2

B=3/4 hours

A=1/2 hours

B=3/4 hours

60 minutes=1 hour

A=1/2 hours

1/2 × 60 minutes

=60/2

=30 minutes

B=3/4 hours

=3/4×60 minutes

=180/4

=45 minutes

Plan A last for 30 minutes

Plan B last for 45 minutes