### 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?

### Why do this problem?

This problem is a quirky puzzle that gives students an opportunity to express algebraically what is known in order to deduce relationships. It is a nice example of a problem that can be solved using algebra but also by finding a neat way to think about the situation.

### Possible approach

This problem could follow on from work on What's it Worth?
Once students have had a chance to think about the problem, take some time to discuss solution methods. One neat way to think about the problem is to realise that passing on three gems and receiving three different gems back leaves each jeweller with one of each gem plus their original collection minus 4...