Difference between revisions of "2017 AMC 8 Problems/Problem 13"

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==Problem 13==
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==Problem==
  
 
Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost 2 games. Emma won 3 games and lost 3 games. If Kyler lost 3 games, how many games did he win?
 
Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost 2 games. Emma won 3 games and lost 3 games. If Kyler lost 3 games, how many games did he win?
  
<math>\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }4</math>
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<math>\textbf{(A) }0\quad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }4</math>
  
 
==Solution==
 
==Solution==
  
Given <math>n</math> games, there must be a total of <math>n</math> wins and <math>n</math> losses. Hence, <math>4 + 3 + K = 2 + 3 + 3</math> where <math>K</math> is Kyler's wins. <math>K = 1.</math>
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Given <math>n</math> games, there must be a total of <math>n</math> wins and <math>n</math> losses. Hence, <math>4 + 3 + K = 2 + 3 + 3</math> where <math>K</math> is Kyler's wins. <math>K = 1</math>, so our final answer is <math>\boxed{\textbf{(B)}\ 1}.</math>
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~CHECKMATE2021
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==Video Solution (CREATIVE THINKING!!!)==
 +
https://youtu.be/4elGw-Ylsxg
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 +
~Education, the Study of Everything
 +
 
 +
==Video Solution by OmegaLearn==
 +
https://youtu.be/6xNkyDgIhEE?t=459
 +
 
 +
~ pi_is_3.14
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 +
==Video Solution==
 +
 
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https://youtu.be/AslL9RYPPy4
 +
 
 +
~hisolver
 +
 
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==See Also==
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{{AMC8 box|year=2017|num-b=12|num-a=14}}
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{{MAA Notice}}

Latest revision as of 17:21, 21 January 2024

Problem

Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost 2 games. Emma won 3 games and lost 3 games. If Kyler lost 3 games, how many games did he win?

$\textbf{(A) }0\quad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }4$

Solution

Given $n$ games, there must be a total of $n$ wins and $n$ losses. Hence, $4 + 3 + K = 2 + 3 + 3$ where $K$ is Kyler's wins. $K = 1$, so our final answer is $\boxed{\textbf{(B)}\ 1}.$ ~CHECKMATE2021

Video Solution (CREATIVE THINKING!!!)

https://youtu.be/4elGw-Ylsxg

~Education, the Study of Everything

Video Solution by OmegaLearn

https://youtu.be/6xNkyDgIhEE?t=459

~ pi_is_3.14

Video Solution

https://youtu.be/AslL9RYPPy4

~hisolver

See Also

2017 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
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

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