Difference between revisions of "1988 AJHSME Problems/Problem 20"

(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==
 
==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 hold when it is full?
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The glass gauge on a [[cylinder|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 hold when it is full?
  
 
<math>\text{(A)}\ 80 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 125 \qquad \text{(D)}\ 130 \qquad \text{(E)}\ 262</math>
 
<math>\text{(A)}\ 80 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 125 \qquad \text{(D)}\ 130 \qquad \text{(E)}\ 262</math>
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==See Also==
 
==See Also==
  
[[1988 AJHSME Problems]]
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{{AJHSME box|year=1988|num-b=19|num-a=21}}
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 22:56, 4 July 2013

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 (ProblemsAnswer KeyResources)
Preceded by
Problem 19
Followed by
Problem 21
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All AJHSME/AMC 8 Problems and Solutions

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