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The admission at an amusement park is $15.50 for children and $20 for adults. On a certain day, 217 people entered the park, and the admission fees collected totaled $3,782. To solve this problem, we set up a system of equations. Let X be the number of children and Y be the number of adults. The total number of people and total fees collected are represented by the equations. By solving the system of equations, we can find out how many children and adults were admitted to the park on that day.