diophantine equation?

please explane how to show my working out in this diophantine equation?

Peter was at a contest and anwered 16 questions. A right awnser is worth 5 points and a wong anwser he loses 3 points. Peter had no points at the end of the game. How many questions did peter get right?

i no the first step is

5x-3(n-x)=0

No, that is NOT the first step. The FIRST step is to define in clearly written statements what your variables mean.

x = Number of correct answers.

You also use 'n', but that is quite unnecessary since you know already that n = 16.

Note: Please don't post the same question multiple times.

Peter was at a contest and anwered 16 questions. A right awnser is worth 5 points and a wong anwser he loses 3 points. Peter had no points at the end of the game. How many questions did peter get right?

What do you know?

1--He answered r right questions and w wrong questions.
2--He andswered 16 questions in all.
3--Therefore, r + w = 16
4--You also know that his total was zero after answering all the questions.
5--Therefore, 5r - 3w = 0

I suspect you can take it from here since it does not involve a single Diophantine equation with 2 unknowns but rather 2 simultaneious equations.