Question

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?

Answer 1

Answer: 10

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 :-

`x+y=30-----(1)\\\\ 10x-5y=0------(2)`

From (2), we have

`5y=10x\\\\\Rightarrow\ y=2x`

Put
`y=2x` in (1)

`x+2x=30\\\\\Rightarrow\ 3x=30\Rightarrow x=10`

Then,
`y=2(10)=20`

Hence, the number of correct problems is 10 and the number of incorrect problems is 20.