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.
