Problem:
Three generous friends, each with some cash, redistribute their money as follows: Ami gives enough money to Jan and Toy to double the amount that each has. Jan then gives enough to Ami and Toy to double their amounts. Finally, Toy gives Ami and Jan enough to double their amounts. If Toy has when they begin and when they end, what is the total amount that all three friends have?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since Toy begins with and her amount is doubled in the first two exchanges, her amounts are , and . This means that she gave away , and this is exactly enough to double the amounts of Ami and Jan. So, the total must be .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions