2020 AMC 12B Problems/Problem 5
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
.
~Argonauts16
Solution 2
Using the information from the problem, we can note that team A has lost of their matches. Using the answer choices, we can find the following list of possible win-lose scenarios for
, represented in the form
for convenience:
Thus, we have 5 matching scenarios, simply adding 7 to
and subtracting 7 from
. We can then test each of the five
scenarios for
and find that
fits this description, making the answer
.
Video Solution
~IceMatrix
See Also
2020 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 4 |
Followed by Problem 6 |
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All AMC 12 Problems and Solutions |
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