Egyptian Math

Mathematics Problems for 12 - 16 year olds

These questions are intended to help illustrate the benefit of using algebra. Parts ‘a’ to ‘d’ may be solved intuitively, or algebraically; but part ‘e’ may only be [easily] solved using algebra.

a) A man borrows donkeys to use for transporting goods.

To re-pay the loan the man must give the lender deben of copper every month per donkey.

The man uses each donkey for days per month for

transporting goods and earns deben of copper per donkey per day for this work.

How many deben of copper does the man make per month?

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b) The donkeys take some looking after, though.
The man has to spend deben of copper per donkey per day for feed. When the donkeys are working they need twice as much feed as they do when they’re resting.

How much does the man have to spend per month to keep the donkeys
(There were days in the ancient Egyptian month and the donkeys are working as described in part [a])

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c) Occasionally the man has to get the donkey doctor to visit if the donkeys get sick.
Over a five-month period the donkey doctor has to visit times the

first month, in the second, times in the third, times the

fourth and in the fifth month.

What is the average number of visits the donkey doctor makes per month?

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d) The donkey doctor charges deben of copper per visit.

Taking into account the amount the man must spend on the loan (part ‘a’) and the feed (part ‘b’), and the amount that the man makes from hiring out the donkeys (part ‘a’),
how much does the man get to keep each month?

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e) If the man needs to earn at least deben of copper per month to

support his family then what is the minimum number of whole days he needs each donkey to work to make enough money?
(assume the donkey doctor makes the same number of visits per month)?

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E-mail me to check your answers.Mark Millmore

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