Difference between revisions of "1958 AHSME Problems/Problem 14"
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| − | After inspection, we notice a general pattern: the <math>n^th</math> boy dances with <math>n + 4</math> girls. | + | After inspection, we notice a general pattern: the <math>n^(th)</math> boy dances with <math>n + 4</math> girls. |
Since the last boy dances with all the girls, there must be four more girls than guys. | Since the last boy dances with all the girls, there must be four more girls than guys. | ||
Revision as of 00:50, 22 December 2015
Problem
At a dance party a group of boys and girls exchange dances as follows: one boy dances with 
girls, a second boy dances with 
girls, and so on, the last boy dancing with all the girls. If 
represents the number of boys and 
the number of girls, then:
Solution
After inspection, we notice a general pattern: the 
boy dances with 
girls.
Since the last boy dances with all the girls, there must be four more girls than guys.
Therefore, the equation that relates them is 
See Also
| 1958 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
