Suppose that a teacher agrees to pay a student 77 ¢ for every problem in this chapter that the student solves correctly, and fines the student 55 ¢ for every problem done incorrectly. If at the end of 4848 problems they do not owe each other any money, how many problems did the student solve correctly?

20 questions

Step-by-step explanation:

Let the number of correctly solved question=x

Let the number of incorrectly solved questions=y

There are 48 problems

Therefore: x+y=48 ... (I)

The teacher pays 7 cents per correct question

The teacher fines the student 5 cents for incorrectly solved questions

Therefore, the teacher pays the student a total of 7x for correctly solved questions

The teacher fines the student a total of 5y for incorrectly solved questions

Since they do not owe each other

7x=5y ... (ii)

We then solve (I) and (ii) simultaneously

x+y=48 ... (I)

7x=5y ... (ii)

From (I), x=48-y

Substitute x=48-y into (ii)

7 (48-y) = 5y

336-7y=5y

336=7y+5y

336=12y

y=336/12=28

From (I)

x=48-y=48-28=20

Therefore the student solved 20 questions correctly.