Difference between revisions of "2017 AMC 8 Problems/Problem 13"
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| − | ==Problem | + | ==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\ | + | <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 / | + | 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> |
| + | ~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== | ==See Also== | ||
| Line 13: | Line 30: | ||
{{MAA Notice}} | {{MAA Notice}} | ||
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
Latest revision as of 18:51, 7 June 2025
Contents
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?
Solution
Given 
games, there must be a total of wins and losses. Hence, 
where 
is Kyler's wins. 
, so our final answer is 
~CHECKMATE2021
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution by OmegaLearn
https://youtu.be/6xNkyDgIhEE?t=459
~ pi_is_3.14
Video Solution
~hisolver
See Also
| 2017 AMC 8 (Problems • Answer Key • Resources) | ||
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
