Difference between revisions of "2017 AMC 8 Problems/Problem 13"
Theopguest (talk | contribs) (→Solution) |
(→Solution) |
||
(12 intermediate revisions by 6 users not shown) | |||
Line 1: | Line 1: | ||
− | ==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== |
Latest revision as of 17:21, 21 January 2024
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.