Simultaneous equations

problem
Favourite

Quadratic Harmony

Age

16 to 18

Challenge level

Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.
problem
Favourite

Surds

Age

14 to 16

Challenge level

Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay
problem
Favourite

Fruity Totals

Age

7 to 16

Challenge level

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
problem
Favourite

Letter Land

Age

11 to 14

Challenge level

If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.
problem
Favourite

Sweet Shop

Age

11 to 14

Challenge level

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.
problem
Favourite

Children at Large

Age

11 to 14

Challenge level

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
problem
Favourite

What's It Worth?

Age

11 to 16

Challenge level

There are lots of different methods to find out what the shapes are worth - how many can you find?
problem
Favourite

Arithmagons

Age

11 to 16

Challenge level

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

Warmsnug Double Glazing

Age

14 to 16

Challenge level

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

Which Is Cheaper?

Age

14 to 16

Challenge level

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?