Difference between revisions of "1988 AJHSME Problems/Problem 20"
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== | ==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? | + | 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== | ||
| − | + | {{AJHSME box|year=1988|num-b=19|num-a=21}} | |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 22:56, 4 July 2013
Problem
The glass gauge on a cylindrical coffee maker shows that there are 
cups left when the coffee maker is 
full. How many cups of coffee does it hold when it is full?
![[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]](http://latex.artofproblemsolving.com/5/8/f/58f83059cccddda489555126f685731af69d8259.png)
Solution
Let the amount of coffee the maker will hold when full be 
. Then, ![\[.36x=45 \Rightarrow x=125 \rightarrow \boxed{\text{C}}\]](http://latex.artofproblemsolving.com/b/5/5/b55cf229fffee16e46f3d6ec911fc931f8a92b7f.png)
See Also
| 1988 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 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. 
