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1988 AJHSME Problems/Problem 20

Revision as of 14:24, 20 April 2009 by 5849206328x (talk | contribs) (New page: ==Problem== The glass gauge on a cylindrical coffee maker shows that there are <math>45</math> cups left when the coffee maker is <math>36\% </math> full. How many cups of coffee does it...)
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Problem

The glass gauge on a cylindrical coffee maker shows that there are $45$ cups left when the coffee maker is $36\%$ full. How many cups of coffee does it hold when it is full?

$\text{(A)}\ 80 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 125 \qquad \text{(D)}\ 130 \qquad \text{(E)}\ 262$

[asy] draw((5,0)..(0,-1.3)..(-5,0)); draw((5,0)--(5,10)); draw((-5,0)--(-5,10)); draw(ellipse((0,10),5,1.3)); draw(circle((.3,1.3),.4)); draw((-.1,1.7)--(-.1,7.9)--(.7,7.9)--(.7,1.7)--cycle); fill((-.1,1.7)--(-.1,4)--(.7,4)--(.7,1.7)--cycle,black); draw((-2,11.3)--(2,11.3)..(2.6,11.9)..(2,12.2)--(-2,12.2)..(-2.6,11.9)..cycle); [/asy]

Solution

Let the amount of coffee the maker will hold when full be $x$. Then, \[.36x=45 \Rightarrow x=125 \rightarrow \boxed{\text{C}}\]

See Also

1988 AJHSME Problems

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