Question

Joanne works two jobs to pay for college. She tutors for $25 per hour and also works as a receptionist for $12 per hour. Due to her class and study schedule, Joanne is only able to work up to 25 hours per week, but must earn at least $200 per week. If t represents the number of hours Joanne tutors and r represents the number of hours she works as a receptionist, which system of inequalities represents this scenario?

A. t + r >= 25
25t + 12r = 200

B. t + r <= 25
25t + 12r <= 200

C. t + r <= 25
25t + 12r >= 200

D. None of the systems shown represent this scenario.

Answer 1

B.
`t+r\leq 25`

`25t+12r\geq 200`

Explanation:

Let t represent the number of hours Joanne tutors and r represents the number of hours Joanne works as a receptionist.

We have been given that Joanne is only able to work up to 25 hours per week. This means t and r will be less than or equal to 25. We can represent this information in an inequality as:

`t+r\leq 25`

We have been given that Joanne tutors for $25 per hour. So earnings from t hours of tutoring would be
`25t`.

She also works as a receptionist for $12 per hour. So earnings from r hours as receptionist would be
`12r`.

Since Joanne must earn at least $200 per week, then earnings from t hours of tutoring and r hours as receptionist must be greater than or equal to 200. We can represent this information in an inequality as:

`25t+12r\geq 200`

Upon looking at our given choices, we can see that option B is the correct choice.