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?

t + r greater than or equal to 25 25t + 12r = 200 t + r less than or equal to 25 25t + 12r less than or equal to 200 t + r less than or equal to 25 25t + 12r greater than or equal to 200 None of the systems shown represent this scenario

Answer 1

The correct option is C:
"t + r <= 25
25t + 12r >= 200"
Because t+R cannot be more than 25 hrs and 25t+12r can be great or equal to $200 because it says she makes at least 200

Answer 2

`t+r\leq 25`

`25t+12r\geq 200`

Explanation:

Let t represents the number of hours Joanne tutors .

Let r represents the number of hours she works as a receptionist.

We are given that Joanne is only able to work up to 25 hours per week

So, inequality becomes:
`t+r\leq 25`

She earns in 1 hour for tutoring = $25

So, She earns in t hour for tutoring = $25t

She earns in 1 hour being receptionist = $12

So, She earns in r hour for receptionist = $12r

Now we are given that she must earn at least $200 per week

So, inequality becomes:
`25t+12r\geq 200`

So, system of inequalities represents this scenario:

`t+r\leq 25`

`25t+12r\geq 200`

So, Option C is correct.