Answer:  The correct option is

(C)~t+rleq 25,\\25t+12rgeq200.

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+rleq 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+12rgeq 25.

Thus, the required system of inequalities representing this scenario is

t+rleq 25,\\25t+12rgeq200.

Option (C) is correct.