Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

Solve the system of equations: ab = 1 bc = 2 cd = 3 de = 4 ea = 6

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?

Triangle ABC is isosceles while triangle DEF is equilateral. Find one angle in terms of the other two.

Can you find the values at the vertices when you know the values on the edges?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

A collection of short Stage 4 problems on equations and formulae.