Mathematics Problems for 12 - 16 year olds

Ancient Egyptian Mathematics Problems No.Three

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?

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])

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?

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?

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)?