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.