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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

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Bang's Theorem

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

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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

Stage: 4 Challenge Level: Challenge Level:1

Hopefully, after a little thought, this becomes fairly straightforward, and is then a good problem about which to ask the question : 'how was the problem made' ?

Students making up problems of this sort for each other to solve will develop a strong sense for equations of straight lines and the algebraic manoeuvres that let us consider their intersection.