Web Analytics
Answered

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?

At + r >= 25

25t + 12r = 200

Bt + r <= 25

25t + 12r <= 200

Ct + r <= 25

25t + 12r >= 200

DNone of the systems shown represent this scenario.

Verified Answer :

JeanaShupp

Answer: C. \(t+r\leq 25\)

\(25t+12r\geq 200\)


Step-by-step 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 =$@@MATH_TOKEN_3@@

Since she must earn $200.

Then \(25t+12r\geq 200\).

Therefore, the required system of inequality will be

\(t+r\leq 25\)

\(25t+12r\geq 200\)

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.