2019 AMC 8
Complete problem set with solutions and individual problem pages
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?
- A.
- B.
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- E.
Solution 1
After Gilda gives % of the marbles to Pedro, she has % of the marbles left. If she then gives % of what's left to Ebony, she has = % of what she had at the beginning. Finally, she gives % of what's left to her brother, so she has of what she had in the beginning left.
Solution 2
WOLG, suppose that Gilda has marbles.
Then, she gives Pedro 20% of , which equals , leaving her with marbles.
Out of marbles, she gives 10% of , which is 8 to Ebony.
Thus, she remains with marbles.
Then, she gives 25% of , which equals to Jimmy, finally leaving her with .
And, =54%=.
