Problem:
Gilda has a bag of marbles. She gives of them to her friend Pedro. Then Gilda gives of what is left to another friend, Ebony. Finally, Gilda gives of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?
Answer Choices:
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E.
Solution:
Imagine that Gilda starts with marbles. She first gives of the marbles to Pedro, leaving her with . She then gives of the marbles to Ebony, leaving her with . Finally Gilda gives of the marbles to Jimmy, leaving her with . Thus Gilda ends up with , which is of the marbles.
After the three gifts, Gilda is left with three-fourths of nine-tenths of four-fifths of the marble she started with, and , which is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions