Bill 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 were 4 clients who did Plan A and 8 who did Plan B. On saturday there were 2 clients who did Plan A and 3 who did Plan B. Bill trained his friday clients for a total of 9 hours and his saturday clients for a total of 4 hours. How long does each of the workout plans last?

The plan A lasts 1.25 hours and plan B lasts 0.5 hours.

Step-by-step explanation:

Let the plan A takes x hours for training and plan B takes y hours for training.

So, from the conditions given we can write two different equations as

4x + 8y = 9 (1) and

2x + 3y = 4 (2)

Now. solving equations (1) and (2) we get,

8y - 6y = 9 - 8

⇒ 2y = 1

⇒ y = 0.5 hours.

Now, from equation (2) we get,

2x = 4 - 3 × 0.5 = 2.5

⇒ x = 1.25 hours.

Therefore, plan A lasts 1.25 hours and plan B lasts 0.5 hours. (Answer)

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

a is the correct