### 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 ##### Age 11 to 14 Challenge Level: A decorator can buy pink paint from two manufacturers. • Paint A is made up from red and white paint in the ratio$1:3$• Paint B is made up from red and white paint in the ratio$1:7$The decorator can mix the paints to produce different shades of pink. If Paint A and Paint B come in the same size cans, what is the least number the decorator would need of each type in order to produce pink paint containing red and white in the following ratios?$1:41:51:6$You may wish to use the interactivity below to check your answers. Another decorator buys pink paint from two different manufacturers: • Paint C is made up from red and white paint in the ratio$1:4$• Paint D is made up from red and white paint in the ratio$1:9$What is the least number the decorator would need of each type in order to produce pink paint containing red and white in the following ratios?$1:51:61:71:8$Once again, you might like to use the interactivity to check your answers. For each of the types of paint, did you have a strategy for mixing the new paint colour? Is it always possible to combine two paints made up in the ratios$1:x$and$1:y$and turn them into paint made up in the ratio$1:z$? (where$x < z < y\$)

You might like to try Mixing More Paints next.