Apple Women Paradox
Each of two apple women had 30 apples for
sale. The first sold hers at the rate of 2 for a nickel, the second
at the rate of 3 for a nickel. At the end of the day their respective
receipts were 75 cents and 50 cents, or $1.25 in all. The
next day the women decided to do business together, so they
pooled their 60 apples and sold them at the rate of 5 for a
dime (2 for a nickel plus 3 for a nickel). Upon counting their
joint receipts at the end of the day they were dismayed to
find that they had only $1.20. They searched all about them
for that other nickel, and wound up by bitterly accusing each
other of having taken it. Where was it?
answer
The apple women made the error of calculating
their average price rate by averaging their individual rates of %
apples a cent and % apples a cent over the same number of apples.
To guarantee the same receipts as those of the first day, they
should have determined their price by dividing the total number
of apples by the total number of cents-that is, 6%25 = 1%5
apples a cent. They actually sold the apples at the rate of 3r2 =
1%4 apples a cent. There’s where the missing nickel went.