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

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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?

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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?

Cereal Mix

Age 11 to 14 Challenge Level:

A farmer is supplying a mix of seeds, nuts and dried apricots to a manufacturer of crunchy cereal bars.

The ingredients cost:
  • dried apricots $£7$ per kg

  • nuts $£6$ per kg

  • seeds $£4$ per kg

He has been asked to supply a mix which costs $£5$ per kg.

What combination of ingredients could he supply?

Is there a relationship between the amounts of each ingredient that he could supply?