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On a certain day, 217 people entered an amusement park, with admission fees totaling $3,782. The fee was $15.50 for children and $20 for adults. To find the number of children and adults admitted, we set up a system of equations. Let X be the number of children and Y be the number of adults. The equation for money collected is 15.50X + 20Y = 3,782, and the equation for the number of people is X + Y = 217. By solving this system, we can determine the number of children and adults admitted.