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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?