Difference between revisions of "2021 AMC 10B Problems/Problem 4"

m
(Removed all unnecessary contents. I merged all contents on the corresponding AMC 12 page.)
(Tag: Replaced)
 
(One intermediate revision by the same user not shown)
Line 1: Line 1:
{{duplicate|[[2021 AMC 10B Problems#Problem 4|2021 AMC 10B #4]] and [[2021 AMC 12B Problems#Problem 2|2021 AMC 12B #2]]}}
+
#REDIRECT [[2021_AMC_12B_Problems/Problem_2]]
 
 
==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?
 
 
 
<math>\textbf{(A)} ~23 \qquad\textbf{(B)} ~32 \qquad\textbf{(C)} ~37 \qquad\textbf{(D)} ~41 \qquad\textbf{(E)} ~64</math>
 
 
 
==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
 
 
 
== Video Solution by OmegaLearn (System of Equations) ==
 
https://youtu.be/hyYg62tT0sY
 
 
 
~ pi_is_3.14
 
 
 
==Video Solution by TheBeautyofMath==
 
https://youtu.be/gLahuINjRzU?t=626
 
 
 
~IceMatrix
 
 
 
==Video Solution by Interstigation==
 
https://youtu.be/DvpN56Ob6Zw?t=286
 
 
 
~Interstigation
 
 
 
==See Also==
 
{{AMC12 box|year=2021|ab=B|num-b=1|num-a=3}}
 
{{AMC10 box|year=2021|ab=B|num-b=3|num-a=5}}
 
{{MAA Notice}}
 

Latest revision as of 05:18, 4 March 2021

Invalid username
Login to AoPS