Answer: 10
Step-by-step explanation:
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 :-
[tex]x+y=30-----(1)\\\\ 10x-5y=0------(2)[/tex]
From (2), we have
[tex]5y=10x\\\\\Rightarrow\ y=2x[/tex]
Put [tex]y=2x[/tex] in (1)
[tex]x+2x=30\\\\\Rightarrow\ 3x=30\Rightarrow x=10[/tex]
Then, [tex]y=2(10)=20[/tex]
Hence, the number of correct problems is 10 and the number of incorrect problems is 20.
