Creating and manipulating expressions and formulae

The mean of three numbers x, y and z is x. What is the mean of y and z?

From this sum of powers, can you find the sum of the indices?

Given that the number 2008 is the correct answer to a sum, can you find n?

Can you work out the value of x in this 'power-full' equation?

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

If a sum invested gains 10% each year how long before it has doubled its value?

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

If $a \times b=2$, $b \times c=24$, $c \times a=3$ and $a$, $b$ and $c$ are positive, what is the value of $a+b+c$?