Suppose that a teacher agrees to pay a student 10¢for every problem in this chapter that the student solves correctly, and fines 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?
Accepted Solution
A:
Answer: 10Step-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.