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Who doesn't love a good concert?

Source: 2022 AIME II Problem 1

February 17, 2022
AMCAIMEAIME II

Problem Statement

Adults made up 512\frac5{12} of the crowd of people at a concert. After a bus carrying 5050 more people arrived, adults made up 1125\frac{11}{25} of the people at the concert. Find the minimum number of adults who could have been at the concert after the bus arrived.