Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7
Can you make a tetrahedron whose faces all have the same perimeter?
A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?
Four jewellers had respectively 8 rubies, 10 sapphires, 100 pearls and 5 diamonds.
Each gave one gem from their collection to each of the rest.
Afterwards they noticed that they all had collections of gems of precisely equal value.
Can you work out the relative values of each gem?
Can you then work out how much each jeweller gained or lost?