### Overturning Fracsum

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

### Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

### Rudolff's Problem

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?

# Matchless

##### Age 14 to 16 Challenge Level:

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?

Did you have more information than you needed to solve the problem?