### 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?

# Negatively Triangular

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

Four straight lines have the following equations:

\begin{align} 3x+8y&=59 \\ x-2y&=1 \\ y-4x&=3 \\ 3y+2x &= -19 \end{align}

How many points of intersections do you expect there to be?

Three of the four lines enclose a triangle which only has negative co-ordinates for all points on that triangle.

Which three lines?