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The admission at the 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 determine the number of children and adults admitted, we set up a system of equations. Let X represent the number of children and Y represent the number of adults. One equation represents the total money collected, and the other represents the total number of people. By solving the system, we can find the values of X and Y.