Assignment brief

Paul and Jenny have a whole number of pounds.

Paul says to Jenny: 'If you give me £3, I will have n times as much as you.'

Jenny says to Paul: 'If you give me £n, I will have 3 times as much as you.

You are given that all these statements are true and that n is a positive integer.

1. Determine an equation for the number of pounds that Jenny has in terms of n.

2. By using long division, or otherwise, on the result in (1) show that n ≤ 7.

3. Hence, by examine cases, determine the values of n for which there is a solution to this problem and in each of these cases the number of pounds Paul and Jenny have.