2010 AMC 10B Problems/Problem 14
We must find the average of the numbers from to
and
in terms of
. The sum of all these terms is
. We must divide this by the total number of terms, which is
. We get:
. This is equal to
, as stated in the problem. We have:
. We can now cross multiply. This gives:
100(100x)=99(50)+x,
10000x=99(50)+x,
9999x=99(50),
101x=50,
This gives us our answer.