Hide answer & extension
If Amy gets \(n\)p for pocket money then brother 1 gets \(\frac{n}{2}\)p, brother 2 gets \(\frac{n}{3}\)p, brother 3 gets \(\frac{n}{4}\)p and brother 4 gets \(\frac{n}{5}\)p.
If Tom is brother 1 and Peter is brother 2, then:
$$\frac{n}{2}-\frac{n}{3}=30$$
$$\frac{n}{6}=30$$
$$n=180$$
If Tom is brother 1 and Peter is brother 3, then:
$$\frac{n}{2}-\frac{n}{4}=30$$
$$\frac{n}{4}=30$$
$$n=120$$
If Tom is brother 1 and Peter is brother 4, then:
$$\frac{n}{2}-\frac{n}{5}=30$$
$$\frac{3n}{10}=30$$
$$n=100$$
If Tom is brother 2 and Peter is brother 3, then:
$$\frac{n}{3}-\frac{n}{4}=30$$
$$\frac{n}{12}=30$$
$$n=360$$
If Tom is brother 2 and Peter is brother 4, then:
$$\frac{n}{3}-\frac{n}{5}=30$$
$$\frac{2n}{15}=30$$
$$n=225$$
If Tom is brother 3 and Peter is brother 4, then:
$$\frac{n}{4}-\frac{n}{5}=30$$
$$\frac{n}{20}=30$$
$$n=600$$
So the possible amounts of money Amy could have received are £1.80, £1.20, £1, £3.60, £2.25 and £6.
Extension
Which values could the 30p be replaced with and still give a whole number of pence for all the possible answers?
