### How Big?

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

### Do Unto Caesar

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won \$1 200. What were the assets of the players at the beginning of the evening?

### Oh for the Mathematics of Yesteryear

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45 days against the siege of the enemy?

# Mixing More Paints

##### Stage: 3 Challenge Level:

Take a look at Mixing Paints .

Experiment with different combinations of paints A and B (and paints C and D). You could use collections of red and white counters to represent the different paints.

Different mixes produce paints that are somewhere in between the shades of paints A and B (or paints C and D).

Imagine a scale representing the shades of pink between paints A and B (or paints C and D).
How do the proportions of the two paints selected determine where the new paint will lie along that scale?

e.g.
• If equal amounts of A and B are mixed, which point along the scale will identify the ratio of red to white of the new paint?
• If the new mix contains twice as much of A than B, where will the point on the scale now be that identifies the new paint?