Difference between revisions of "2021 AMC 10B Problems/Problem 4"
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| − | + | ==Problem== | |
| + | At a math contest, <math>57</math> students are wearing blue shirts, and another <math>75</math> students are wearing yellow shirts. The 132 students are assigned into <math>66</math> pairs. In exactly <math>23</math> of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yellow shirts? | ||
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| + | <math>\textbf{(A)} ~23 \qquad\textbf{(B)} ~32 \qquad\textbf{(C)} ~37 \qquad\textbf{(D)} ~41 \qquad\textbf{(E)} ~64</math> | ||
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| + | ==Solution== | ||
| + | There are <math>46</math> students paired with a blue partner. The other <math>11</math> students wearing blue shirts must each be paired with a partner wearing a shirt of the opposite color. There are <math>64</math> students remaining. Therefore the requested number of pairs is <math>\tfrac{64}{2}=\boxed{\textbf{(B)} ~32}</math> ~Punxsutawney Phil | ||
Revision as of 17:32, 11 February 2021
Problem
At a math contest, 
students are wearing blue shirts, and another 
students are wearing yellow shirts. The 132 students are assigned into 
pairs. In exactly 
of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yellow shirts?
Solution
There are 
students paired with a blue partner. The other 
students wearing blue shirts must each be paired with a partner wearing a shirt of the opposite color. There are 
students remaining. Therefore the requested number of pairs is 
~Punxsutawney Phil
