MathDB
broken painted bottles

Source: 2022 Paraguayan Mathematical Olympiad L3 p4 - OMAPA

October 24, 2022
algebranumber theory

Problem Statement

Karina, Leticia and Milena paint glass bottles and sell them as decoration. they had 100100 bottles, and they decorated them in such a way that each bottle was painted by a single person. After the finished, they put all the bottles on a table. In an oversight one of them pushed the table, falling and breaking exactly 18\frac18 of the bottles that Karina painted, 13\frac13 of the bottles that Milena, painted and 16\frac16 of the bottles that Leticia painted. In total, 8282 painted bottles remained unbroken. Knowing that the number of broken bottles that Milena had painted is equal to the average of the amounts of broken bottles painted by Karina and Leticia, how many bottles did each of them paint?