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Hi Garth,

I would use algebra to solve this problem.

Suppose the learner solved p problems correctly. He got R8 for each problem he solved correctly and hence he received R8 × p.

For how many did he give an incorrect solution? He received a fine of R5 for each incorrect solution so what was his total fine?

Since neither the learner nor the teacher owed money at the end the amount the learner received was equal to his total fine. Solve for p.

Penny

Garth,

I'm going to suggest an old-fashioned method that some 19th century school textbooks used to teach. It can be used for a lot of problems like this one.

Can you find _some_ M and N such that M wrong answers balance N right answers? (Hint: play around with the numbers in the original problem.) For what total number of problems would this be a correct answer?

Now scale this solution to get a solution to the real problem.

Good Hunting!
RD