Difference between revisions of "2010 AMC 8 Problems/Problem 12"
(Created page with "Since 80 percent of the 500 balls are red, there are 400 red balls. Therefore, there must be 100 blue balls. For the 100 blue balls to be 25% or 1/4 of the bag, there must be 400...") |
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| − | Since 80 percent of the 500 balls are red, there are 400 red balls. Therefore, there must be 100 blue balls. For the 100 blue balls to be 25% or 1/ | + | ==Problem== |
| + | Of the <math>500</math> balls in a large bag, <math>80%</math> are red and the rest are blue. How many of the red balls must be removed so that <math>75%</math> of the remaining balls are red? | ||
| + | <math> \textbf{(A)}\ 25\qquad\textbf{(B)}\ 50\qquad\textbf{(C)}\ 75\qquad\textbf{(D)}\ 100\qquad\textbf{(E)}\ 150 </math> | ||
| + | |||
| + | ==Solution== | ||
| + | Since 80 percent of the 500 balls are red, there are 400 red balls. Therefore, there must be 100 blue balls. For the 100 blue balls to be 25% or <math>\dfrac{1}{4}</math> of the bag, there must be 400 balls in the bag so 100 red balls must be removed. The answer is <math>\boxed{\textbf{(D)}\ 100}</math>. | ||
Revision as of 17:36, 5 November 2012
Problem
Of the 
balls in a large bag, $80%$ (Error compiling LaTeX. Unknown error_msg) are red and the rest are blue. How many of the red balls must be removed so that $75%$ (Error compiling LaTeX. Unknown error_msg) of the remaining balls are red?
Solution
Since 80 percent of the 500 balls are red, there are 400 red balls. Therefore, there must be 100 blue balls. For the 100 blue balls to be 25% or 
of the bag, there must be 400 balls in the bag so 100 red balls must be removed. The answer is 
.
