2019 AMC 8 Problems/Problem 8

Problem

Gilda has a bag of marbles. She gives $20\%$ of them to her friend Pedro. Then Gilda gives $10\%$ of what is left to another friend, Ebony. Finally, Gilda gives $25\%$ 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?

$\textbf{(A) }20\qquad\textbf{(B) }33\frac{1}{3}\qquad\textbf{(C) }38\qquad\textbf{(D) }45\qquad\textbf{(E) }54$

Solution 1

After Gilda gives $20$ % of the marbles to Pedro, she has $80$ % of the marbles left. If she then gives $10$ % of what's left to Ebony, she has $(0.8*0.9)$ = $72$ % of what she had at the beginning. Finally, she gives $25$ % of what's left to her brother, so she has $(0.75*0.72)$ $\boxed{\textbf{(E)}\ 54}$ of what she had in the beginning left.

Solution 2

WOLG, suppose that Gilda has $100$ marbles.

Then, she gives Pedro 20% of $100$ , which equals $20$ , leaving her with $80$ marbles.

Out of $80$ marbles, she gives 10% of $80$ , which is 8 to Ebony.

Thus, she remains with $72$ marbles.

Then, she gives 25% of $72$ , which equals $18$ to Jimmy, finally leaving her with $54$ .

And, $\frac{54}{100}$ =54%= $\boxed{\textbf{(E)}\ 54}$ .

~phoenixfire

Solution 3

(Only if you have lots of time do it this way) Since she gave away 20% and 10% of what is left and then another 25% of what is actually left, we can do 20+10+25 or 55%. But it is actually going to be a bit more than 55% because 10% of what is left is not 10% of the total amount. So, the only option that is greater than 100% - 55% is $\boxed{\textbf{(E)}\ 54}$ .

Video Solution

Video Solution by Math-X (Do percentage questions like this!!!)

https://youtu.be/IgpayYB48C4?si=_eGyqshtrNAg3tAm&t=2362

~Math-X

The Learning Royal : https://youtu.be/8njQzoztDGc

Video Solution 2

Solution detailing how to solve the problem: https://www.youtube.com/watch?v=WAmvVQzuzfc&list=PLbhMrFqoXXwmwbk2CWeYOYPRbGtmdPUhL&index=9

Video Solution 3

https://youtu.be/Cwnq8XRxJ6Y Soo, DRMS, NM

Video Solution 4

https://youtu.be/eApJGrvDT5U

~savannahsolver

Video Solution (CREATIVE THINKING!!!)

https://youtu.be/yAdewhYZ3Uc

~Education, the Study of Everything

Video Solution by The Power of Logic(1 to 25 Full Solution)

https://youtu.be/Xm4ZGND9WoY

~Hayabusa1

2019 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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