Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

(→‎Solution 1)
(→‎Solution 1)
Line 5: Line 5:
  
 
==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) = 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.~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.~heeeeeeeheeeeee
  
 
==Solution 2==
 
==Solution 2==

Revision as of 11:48, 21 November 2019

Problem 8

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 $80%$ (Error compiling LaTeX. Unknown error_msg) 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.~heeeeeeeheeeeee

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

See Also

2019 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 7 		Followed by
Problem 8
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. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2019_AMC_8_Problems/Problem_8&oldid=111939"