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.

A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.

Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.