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On a certain day, 217 people entered an amusement park, with admission fees totaling $3,782. With children's admission at $15.50 and adults at $20, the task is to determine the number of children and adults admitted. Using X for children and Y for adults, one equation represents the total fees collected, while the second equation signifies the total number of people. Through setting up and solving this system of equations, one can determine the number of children and adults who entered the park on that day.