Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

algebra intermediate

Problem

Al, Betty, and Clare split \1000\. Betty and Clare have both doubled their money, whereas Al has managed to lose \100$. What was Al's original portion?
Solution
Denote the original portions for Al, 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 .
Final answer
400