Hi, I'm new here just signed up. I got a problem for homework that's been troubling me so I did a quick google for math help forums and came up with this place. Any help you give me is MUCH appreciated, I also hope I posted this in the right area.

Anyway here is the question:

*Peter entered a competition in which he got 5 points for every correct answer, but lost 3 points for every wrong answer. At the end of the competition he had no points at all and had answered 16 questions.*
That was basically the first statement. Then we had to work out this problem:

*Work out how many questions Peter got right from the 16 questions he answered.*
I did this correctly, I think.

X questions wrong @ -3 points ea.

16 - X questions right @ 5 points ea.

-3x + 5 (16 - x) = 0

-3x + 80 - 5x = 0

-8x = -80

x = 10.

I'm fairly sure that I got that question right, but further down the track came this question;

*What numbers of questions could you answer to end up with no points?*
I thought that I could use the same formula in a way as the first question, so I used this:

Let there be N questions where 0 > n

__>__ 20

Let the number of correct answers = X @ 5 points ea.

Therefore, let the number wrong = n - x. @ -3 points ea.

5x - 3 (n - x) = 0

Now I'm a bit confused. If I keep working it out I'll get something like this:

5x - 3n - 3x = 0

2x - 3n = 0

Now I guess I should take one of these to the other side of the equation.

2x = 3n

Now I'm totally stumped. The teacher said you'd have to use some guesswork to get the answer, but I have no idea how you could do that either.

Am I missing out on something? How do you do this?

Thanks for the help.