Difference between revisions of "2020 AMC 12B Problems/Problem 5"
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We can solve through substitution, as the second equation can be written as <math>x=3y-7</math>, and plugging this into the first equation gives <math>5y=6y-7\implies y=7</math>, which means <math>x=3(7)-7=14</math>. Finally, we want the total number of games team <math>A</math> has played, which is <math>A_g=3(14)=\boxed{\textbf{(C) } 42}</math>. | We can solve through substitution, as the second equation can be written as <math>x=3y-7</math>, and plugging this into the first equation gives <math>5y=6y-7\implies y=7</math>, which means <math>x=3(7)-7=14</math>. Finally, we want the total number of games team <math>A</math> has played, which is <math>A_g=3(14)=\boxed{\textbf{(C) } 42}</math>. | ||
+ | |||
+ | ==Video Solution== | ||
+ | https://youtu.be/WfTty8Fe5Fo | ||
+ | |||
+ | ~IceMatrix | ||
==See Also== | ==See Also== |
Revision as of 02:30, 8 February 2020
Contents
Problem
Teams and
are playing in a basketball league where each game results in a win for one team and a loss for the other team. Team
has won
of its games and team
has won
of its games. Also, team
has won
more games and lost
more games than team
How many games has team
played?
Solution
First, let us assign some variables. Let
where denotes number of games won,
denotes number of games lost, and
denotes total games played for
. Using the given information, we can set up the following two equations:
We can solve through substitution, as the second equation can be written as , and plugging this into the first equation gives
, which means
. Finally, we want the total number of games team
has played, which is
.
Video Solution
~IceMatrix
See Also
2020 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 4 |
Followed by Problem 6 |
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 AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.