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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?

Respuesta :

Answer:

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.

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