### 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

### Bang's Theorem

If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.

### 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?

# Surds

##### Stage: 4 Challenge Level:

Find the exact values of $x$, $y$ and $a$ satisfying the following system of equations:
\begin{align}
\frac{1}{a+1}&=a-1 \\
x+y&=2a \\
x&=ay
\end{align}