Simultaneous equations

The sum of any two of the numbers 2, 34 and 47 is a perfect square. Choose three square numbers and find sets of three integers with this property. Generalise to four integers.

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.

Can you find the value of t in these equations?

Find out how to model a battery mathematically

What does the sum of these three numbers tell us about their product?

To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?

Solve the system of equations xy = 1 yz = 4 zx = 9

Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.

A table has blocks of wood placed on and next to it. Can you work out how tall it is?

Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.