2022 Spring LMT Team 1
Source:
September 1, 2022
algebrageometry
Problem Statement
Derek and Jacob have a cake in the shape a rectangle with dimensions inches by inches. They make a deal to split it: Derek takes home the portion of the cake that is less than one inch from the border, while Jacob takes home the remainder of the cake. Let be the ratio of the amount of cake Derek took to the amount of cake Jacob took, where and are relatively prime positive integers. Find .