Question

Jake plans to take a summer job at the recreation center as a lifeguard. He can be paid according to two different plans.

Plan A: $300 per week
Plan B: $150 per week plus $6.25 per hour

How many hours will Jake have to work to make more money with Plan B then Plan A?

9. Write an inequality. Let x represent the number of hours Jake works.
Answer: _____

10. Solve the inequality.
Answer: _____

I know the answer which is 25 hours because if he worked 24 hours he would make the same as Plan A provides. My problem is I don’t know how to show my work. Can anyone help please?

Answer 1

Payment on Plan A = $300

x is the number of hours Jake works.

Payment on Plan B = Fixed charges + (charge per hour) × (number of hours worked)

                               = $150 + $6.25(x)

                               = 150 + 6.25x

Since, the payment on Plan B should be more than Plan A,

150 + 6.25x > 300

6.25x > 300 - 150

6.25x > 150

$x > \frac{150}{6.25}$

x > 24

The minimum vale for x which satisfies this inequality is 25.

Hence, x = 25.