Difference between revisions of "2019 AMC 8 Problems/Problem 8"

Latest revision as of 09:30, 9 November 2024

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

Suppose Gilda has 100 marbles.

Then, she gives Pedro 20% of 100 = 20, she remains with 80 marbles.

Out of 80 marbles, she gives 10% of 80 = 8 to Ebony.

Thus, she remains with 72 marbles.

Then, she gives 25% of 72 = 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

@@ Line 1: / Line 1: @@
-==Problem 8==
+==Problem==
 Gilda has a bag of marbles. She gives <math>20\%</math> of them to her friend Pedro. Then Gilda gives <math>10\%</math> of what is left to another friend, Ebony. Finally, Gilda gives <math>25\%</math> 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?
@@ Line 5: / Line 5: @@
 ==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) <math>\boxed{\textbf{(E)}\ 54}</math>. of what she had in the beginning left.~heeeeeeeheeeeee
+After Gilda gives <math>20</math>% of the marbles to Pedro, she has <math>80</math>% of the marbles left. If she then gives <math>10</math>% of what's left to Ebony, she has <math>(0.8*0.9)</math> = <math>72</math>% of what she had at the beginning. Finally, she gives <math>25</math>% of what's left to her brother, so she has <math>(0.75*0.72)</math> <math>\boxed{\textbf{(E)}\ 54}</math> of what she had in the beginning left.
 ==Solution 2==
 Suppose Gilda has 100 marbles.
-Then she gives Pedro 20% of 100 = 20, she remains with 80 marbles.
+Then, she gives Pedro 20% of 100 = 20, she remains with 80 marbles.
-Out of 80 marbles she gives 10% of 80 = 8 to Ebony.
+Out of 80 marbles, she gives 10% of 80 = 8 to Ebony.
-Thus she remains with 72 marbles.
+Thus, she remains with 72 marbles.
-Then she gives 25% of 72 = 18 to Jimmy, finally leaving her with 54.
+Then, she gives 25% of 72 = 18 to Jimmy, finally leaving her with 54.
-And \frac{54}{100} = 54% = <math>\boxed{\textbf{(E)}\ 54}</math>
+And, <math>\frac{54}{100}</math>=54%=<math>\boxed{\textbf{(E)}\ 54}</math>.
 ~phoenixfire
-==See Also==
+==Solution 3==
-{{AMC8 box|year=2019|num-b=7|num-a=8}}
+(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 <math>\boxed{\textbf{(E)}\ 54}</math>.
+== 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
+==See also==
+{{AMC8 box|year=2019|num-b=7|num-a=9}}
 {{MAA Notice}}

2019 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
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