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

Answer: The correct option is

`(C)~t+r\leq 25,\\\\25t+12r\geq200.`

Step-by-step explanation: Given that Joanne works two jobs to pay for college.

Let, t and r represents the number of hours she tutors and number of hours she works as a receptionist.

The, the total number of hours she work = t + r.

Since she can work up to 25 hours per week, so the total number of hours she work is less than or equal to 25.

Therefore, we can write

`t+r\leq 25.`

Now,

Joanne earns $25 per hour through tutoring, so the amount of money she earn tutoring = $25t,

and

she earn $12 working as a receptionist, so the amount of money she earn as a receptionist = $12r.

Since she earn at lest $200 per week, so the total earning of Joanne per week will be greater than or equal to $200.

Therefore, we can write

`25t+12r\geq 25.`

Thus, the required system of inequalities representing this scenario is

`t+r\leq 25,\\\\25t+12r\geq200.`

Option (C) is correct.

Answer 2

Answer: C.
`t+r\leq 25`

`25t+12r\geq 200`

Explanation:

If 't' represents the number of hours Joanne tutors and 'r' represents the number of hours she works as a receptionist.

Then the total hours she can work=t+r

Since she can work up to 25 hours.

Thus
`t+r\leq 25`

If she earns $25 per hour by tuition and $ 12 per hour by working as a receptionist .

Then her total earning =$
`25t+12r`

Since she must earn $200.

Then
`25t+12r\geq 200`.

Therefore, the required system of inequality will be

`t+r\leq 25`

`25t+12r\geq 200`