Difference between revisions of "1987 AJHSME Problems/Problem 18"
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{{AJHSME box|year=1987|num-b=17|num-a=19}} | {{AJHSME box|year=1987|num-b=17|num-a=19}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
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Revision as of 22:53, 4 July 2013
Problem
Half the people in a room left. One third of those remaining started to dance. There were then 
people who were not dancing. The original number of people in the room was
Solution
Let the original number of people in the room be 
. Half of them left, so 
of them are left in the room.
After that, one third of this group is dancing, so 
people are not dancing.
This is given to be , so ![\[\frac{x}{3}=12\Rightarrow x=36\]](http://latex.artofproblemsolving.com/7/8/3/783c0b7a3c13d6d8ec3fcef9d13a4b6db510f949.png)
See Also
| 1987 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 17 |
Followed by Problem 19 | |
| 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. 
