Problem 1
A farmer is selling apples at the market. To the first customer, he sells half of all of his apples then half of one apple. To the second customer, he sells half of all of his remaining apples then half of one apple. To the third customer, he sells half of all of his remaining apples then half of one apple etc. To the 7th customer he sells half of the apples he has left then half of one apple. The farmer has now run out of apples.
How many apples did the farmer have when he started?
Solution
If the total number of apples is
x,
then the number of apples the first customer bought is:
The number of apples the second
customer bought is:
The number of apples the third customer
bought is:
The number of apples the seventh
customer bought is:
We now have the equation:
=
x=127 (So the farmer initially
had 127 apples).
