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==Problem 8== | ==Problem 8== | ||
| − | Gilda has a bag of marbles. She gives <math>20\%</math> of them to her friend Pedro. Then Gilda gives <math>10\%</math> of | + | Gilda has a bag of marbles. She gives <math>20\%</math> of them to her friend Pedro. Then Gilda gives <math>10\%</math> of the original to another friend, Ebony. Finally, Gilda gives <math>25\%</math> of the original in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself? |
<math>\textbf{(A) }20\qquad\textbf{(B) }33\frac{1}{3}\qquad\textbf{(C) }38\qquad\textbf{(D) }45\qquad\textbf{(E) }54</math> | <math>\textbf{(A) }20\qquad\textbf{(B) }33\frac{1}{3}\qquad\textbf{(C) }38\qquad\textbf{(D) }45\qquad\textbf{(E) }54</math> | ||
==Solution 1== | ==Solution 1== | ||
| − | 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> | + | 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== | ==Solution 2== | ||
Suppose Gilda has 100 marbles. | 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 <math>\frac{54}{100}</math>=54%=<math>\boxed{\textbf{(E)}\ 54}</math> | + | And, <math>\frac{54}{100}</math>=54%=<math>\boxed{\textbf{(E)}\ 54}</math>. |
~phoenixfire | ~phoenixfire | ||
| − | ==Solution 3== (Only if you have lots of time do it this way) | + | ==Solution 3== |
| − | 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>. | + | (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>. | ||
| − | ==See | + | == 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(Problem 1 to 25 Full Solution)== | ||
| + | https://youtu.be/Xm4ZGND9WoY | ||
| + | |||
| + | ~Hayabusa1 | ||
| + | |||
| + | ==See also== | ||
{{AMC8 box|year=2019|num-b=7|num-a=9}} | {{AMC8 box|year=2019|num-b=7|num-a=9}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 12:37, 11 June 2024
Contents
- 1 Problem 8
- 2 Solution 1
- 3 Solution 2
- 4 Solution 3
- 5 Video Solution
- 6 Video Solution by Math-X (Do percentage questions like this!!!)
- 7 Video Solution 2
- 8 Video Solution 3
- 9 Video Solution 4
- 10 Video Solution (CREATIVE THINKING!!!)
- 11 Video Solution by The Power of Logic(Problem 1 to 25 Full Solution)
- 12 See also
Problem 8
Gilda has a bag of marbles. She gives 
of them to her friend Pedro. Then Gilda gives 
of the original to another friend, Ebony. Finally, Gilda gives 
of the original in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?
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
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, 
=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 .
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
~savannahsolver
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution by The Power of Logic(Problem 1 to 25 Full Solution)
~Hayabusa1
See also
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
