### 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 Paints ##### Stage: 3 Challenge Level: A problem that challenges students to consider the effect of combining ratios. The problem assumes that students understand ratios (they understand that if$1/3$is red it does not mean that the ratio of red to white is$1:3\$) and are able to simplify ratios.

A possible start to using this problem in a classroom could involve asking students to suggest possible combinations of paints A and B (or C and D) and their suggestions could be written up for all to see.

It may be useful to provide students with red and white counters so that they can simulate the effect of mixing the paints. However, counters must be used with care; students need to understand that they must have the same overall number of counters for each paint mixture.

Possible follow up questions:
• What is the ratio of red to white paint in these mixes?
• Can any of these ratios be simplified?
• Will any of these combinations produce the same shade of pink?
• Can you list the mixes in order as they become paler?
Mixing More Paints is a follow-up question to this one.