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.