2015 AMC 8 Problems/Problem 24
A baseball league consists of two four-team divisions. Each team plays every other team in its division games. Each team plays every team in the other division
games with
and
. Each team plays a 76 game schedule. How many games does a team play within its own division?
Solution 1
On one team they play games in their division and
games in the other. This gives
Since we start by trying
. This doesn't work because
is not divisible by
.
Next, does not work because
is not divisible by
We try this does work giving
and thus
games in their division.
Solution 2
, giving
.
Since
, we have
.
Since
is
, we must have
equal to
, so
.
This gives , as desired. The answer is
.
See Also
2015 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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