Difference between revisions of "2004 AMC 10A Problems/Problem 13"
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At a party, each man danced with exactly three women and each woman danced with exactly two men. Twelve men attended the party. How many women attended the party? | At a party, each man danced with exactly three women and each woman danced with exactly two men. Twelve men attended the party. How many women attended the party? | ||
| − | <math> \mathrm{(A) \ } 8 \qquad \mathrm{(B) \ } 12 \qquad \mathrm{(C) \ } 16 \qquad \mathrm{(D) \ } 18 | + | <math> \mathrm{(A) \ } 8 \qquad \mathrm{(B) \ } 12 \qquad \mathrm{(C) \ } 16 \qquad \mathrm{(D) \ } 18 \qquad \mathrm{(E) \ } 24 </math> |
==Solution== | ==Solution== | ||
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*[[2004 AMC 10A Problems/Problem 14|Next Problem]] | *[[2004 AMC 10A Problems/Problem 14|Next Problem]] | ||
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| + | [[Category:Introductory Algebra Problems]] | ||
Revision as of 11:11, 5 November 2006
Problem
At a party, each man danced with exactly three women and each woman danced with exactly two men. Twelve men attended the party. How many women attended the party?
Solution
If each man danced with 3 women, then there were a total of 
pairs of a man and a women. However, each women only danced with 2 men, so there must have been 
women 
.
