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The admission fees at the amusement park were $15.50 for children and $20 for adults. 217 people entered the park, collecting a total of $3,782. To find out how many children and adults were admitted, we set up a system of equations. Let X represent the number of children and Y the number of adults. With the given information, one equation represents the total money collected and the other represents the number of people admitted. By solving this system, we can determine the number of children and adults who entered the park that day.