### Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

### 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?

# Tray Bake

##### Stage: 3 Challenge Level:
Start from the information given for 12 cakes.

12 cakes cost 65p.
For 24 cakes, double the cost is £1.30.
For 36 cakes, the cost of 12 cakes multiplied by 3 is £1.95.
For 6 cakes, half the cost is not 32.5p, since we no longer have half pence in the UK.  The cost is therefore 33p.

For the ingredients:

 Ingredients 12 cakes 24 cakes 36 cakes 6 cakes 1 cake Caster sugar 130g 260g 390g 65g 10.8g Margarine 130g 260g 390g 65g 10.8g Self raising flour 130g 260g 390g 65g 10.8g Eggs 2 4 6 1 1/3 Baking powder (5ml spoons) 1 2 3 1/2 1/12

To scale the recipe for other numbers of cakes which are not a simple multiple of 12 or 6, you will need to find the cost of 1 cake and the amount of ingredients required for 1 cake.  Then multiply by the number of cakes required, rounding your answers sensibly and remembering that eggs come in whole numbers!  (Professional kitchens weigh the eggs, rather than using whole numbers of eggs.)

If you are using the provided arrows, these facts may help you:
• use x2 (doubling) arrows going from 6 cakes to 12 and from 12 cakes to 24
• use divide by 2 or multiply by 1/2 (halving, same thing as division and multiplication are inverse processes,and 1/2 is the inverse of 2) arrows for 12 cakes to 6 or 24 cakes to 12
• use x 1.5 or x3/2 or half as much again cards going from 24 cakes to 36
• use divide by 1.5 or x2/3 cards going from 36 cards to 24