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

Plan A last for 30 minutes

Plan B last for 45 minutes

Step-by-step 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

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step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true