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THE EGG FARMER
by Bill Graham
Farmer Humphrey, who loves eggs and fractions,
sells 1/2 of his present number of eggs plus 1/2 of an egg
to each of his customers until he sells all of his eggs.
That is, his first customer buys 1/2 of the original number of eggs
plus 1/2 an egg, the next customer buys half of the remaining eggs plus half an egg,
etc. (the first customer buys the most eggs and his last customer buys the fewest,
leaving none).
If Farmer Humphrey had seven customers, how many eggs did he sell or start with?
(Even though the farmer loves fractions, none of the customers likes broken eggs.)
One more time
Rethink the problem replacing 1/2 with a/b, any other fraction.
In other words, Farmer Humphrey sells a/b of the original number of eggs
to the first customer plus a/b of an egg, etc.
What can you figure out about a and b and the original number of eggs
that Farmer Humphrey started with (or sold)?
Vol 2, No 1
Farmer Humphrey, who loves eggs and fractions,
sells 1/2 of his present number of eggs plus 1/2 of an egg
to each of his customers until he sells all of his eggs.
That is, his first customer buys 1/2 of the original number of eggs
plus 1/2 an egg, the next customer buys half of the remaining eggs plus half an egg,
etc. (the first customer buys the most eggs and his last customer buys the fewest,
leaving none).
If Farmer Humphrey had seven customers, how many eggs did he sell or start with?
(Even though the farmer loves fractions, none of the customers likes broken eggs.)
Rethink the problem replacing 1/2 with a/b, any other fraction.
In other words, Farmer Humphrey sells a/b of the original number of eggs
to the first customer plus a/b of an egg, etc.
What can you figure out about a and b and the original number of eggs
that Farmer Humphrey started with (or sold)?