Creating and manipulating expressions and formulae

A rectangular plank fits neatly inside a square frame when placed diagonally. What is the length of the plank?

A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?

The square of a number is 12 more than the number itself. The cube of the number is 9 times the number. What is the number?

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 $a+b+c$?

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?”

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

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

Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?

Can you work out Ali's age based on the diagram?