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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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Building Tetrahedra

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

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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?

Day of the Triffids

Age 14 to 16 Short Challenge Level:

Jasmine spends exactly £120 on three types of plants.

Poison ivy plants cost £2 each.
Deadly nightshade plants cost £9 each.
Triffids plants cost £12 each.

She buys twenty plants in total, including at least one of each type.

How many triffids did she buy?
 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.