Problem:
Al, Betty, and Clare split among them to be invested in different ways. Each begins with a different amount. At the end of one year they have a total of . Betty and Clare have both doubled their money, whereas Al has managed to lose . What was Al's original portion?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Denote the original portions for , Betty, and Clare as , and , respectively. Then
Substituting in the second equation, we have
This yields , which is Al's original portion.
Note that although we know that , we have no way of determining either or .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions