### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

The ratio $a : b = 2 :3$ and the ratio $a : c = 3 : 4$. What is the ratio $b : c$?                                                                                                                                                                                                                         If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.