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The amusement park charges $15.50 for children and $20 for adults. 217 people entered the park and $3,782 was collected. Let X be the number of children and Y be the number of adults. The total fees collected and the number of people entering the park are represented by two equations. The first equation represents the money collected and the second equation represents the number of people entering the park. By setting up and solving this system of equations, we can find out how many children and adults entered the park.