### 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.

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# CD Heaven

##### Stage: 4 Challenge Level:

All CD Heaven stores were given the same number of a popular CD to sell for $£24$.

In their two week sale each store reduces the price of the CD by $25\%$ and any further reductions are then left to the discretion of the store managers.

Towards the end of the two week sale one store still had $30$ CDs left and the manager decided to try to clear the remainder by reducing the price by a further $1/3$ but still did not manage to sell them all. The total sales for the CDs was $£2010$. If the store had managed to sell all its CDs by the end of the two week sale period it would have received $£2370$.

Another store sold the same number of CDs before and during the first two weeks of the sale as the first store but in reverse order (the number they sold for $£24$ was the same as the number sold in the two weeks of the sale by the first store and vice versa). At the end of the two weeks the shop manager decided to reduce the price of the CDs by a further $50\%$ and managed to sell all the remaining $30$ CDs making her total sales $£2010$.

How many CDs did the first store sell at each price?