Simultaneous equations

problem
Leonardo's problem

Age

14 to 18

Challenge level

A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?
problem
How many balls?

Age

16 to 18

Challenge level

A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.
problem
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
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
CD Heaven

Age

14 to 16

Challenge level

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?
problem
All square

Age

11 to 14

Challenge level

Solve the system of equations xy = 1 yz = 4 zx = 9
problem
Pareq calc

Age

14 to 16

Challenge level

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel lines are 1 unit and 2 units.
problem
Symmetricality

Age

14 to 18

Challenge level

Five equations and five unknowns. Is there an easy way to find the unknown values?
problem
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
Whole numbers only

Age

11 to 14

Challenge level

Can you work out how many of each kind of pencil this student bought?