Creating and Solving Equation from Word Problem

Question

I have this word problem that I cannot figure out how to put into an equation:

Suppose that we agree to pay you $9$ cents for every math problem you solved correctly, and fine you $5$ cents for every problem done incorrectly. If at the end of $42$ questions, we do not owe each other any money, how many problems did you solve correctly?

I know the solution is $15$, but I did not solve it with an equation. I need help figuring out how to organize this into an equation.

Answer 1

Since the question is asking how many problems you solved correctly, then set

$x$= number of questions solved correctly

given the total number of questions is 42, the number of incorrectly solved questions is $(42-x)$

then, the money will work as: you gained $9x$ cents for correctly solved, and $-5*(42-x)$ cents is the money you lost for incorrect.

provided that "we do not owe each other money", the sum of gain and loss is $0$ cents.

hence a equation of the sum of gain and loss is: $ 0 = 9x -5*(42-x)$. then solve this equation to get $x$.