Suppose that a teacher agrees to pay a student 10¢for every problem in this chapter that the student solves correctly, and fin
es the student 5¢for every problem done incorrectly. If at the end of 30problems they do not owe each other any money, how many problems did the student solve correctly?
Let x be the number of correct problems and y be the number of incorrect problems.
Given: A teacher pays a student 10¢ for every problem in this chapter that the student solves correctly, and fines the student 5 ¢ for every problem done incorrectly.
At the end of 30 problems they do not owe each other any money.
The by considering the given information we have the following equations :-
From (2), we have
Put in (1)
Then,
Hence, the number of correct problems is 10 and the number of incorrect problems is 20.