Difference between revisions of "2015 AMC 8 Problems/Problem 24"
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We try <math>M=7</math> this does work giving <math>N=16,~M=7</math> and thus <math>3\times 16=\boxed{\textbf{(B)}~48}</math> games in their division. | We try <math>M=7</math> this does work giving <math>N=16,~M=7</math> and thus <math>3\times 16=\boxed{\textbf{(B)}~48}</math> games in their division. | ||
− | <math>M=10</math> seems to work,until we realize this gives <math>N=12</math>, but <math>N>2M</math> so this will not work. | + | <math>M=10</math> seems to work, until we realize this gives <math>N=12</math>, but <math>N>2M</math> so this will not work. |
==Solution 2== | ==Solution 2== |
Revision as of 14:58, 1 June 2019
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.
seems to work, until we realize this gives
, but
so this will not work.
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 | |
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 |
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