Age 7 to 11 Challenge Level:
We had these submissions from Colwich Primary School:
Ben and Will
There are six windows shown and you could put them in pairs of windows which have the same perimeter but different areas, or the same areas but different perimeters.
We chose to work with the £150 and £140 windows which have the same perimeter, but different areas.
For the £150 window, A = 9 and P = 12. For the £140 window, A = 8 and P = 12.
This showed us that 1 square of A = £10.
For the £140 window, this means that A = £80 and P = £60, which means that 1P = £5.
So the answer is that a piece of glass costs £10 for every square of area, plus £5 for every square edge.
We checked our answers on all the other pieces of glass, and it worked every time.
Thank you very much for these submissions.