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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 total admission fees collected were $3,782. To find out how many children and how many adults were admitted, we set up a system of equations. Let X be the number of children and Y be the number of adults. The fee for children is $15.50 and for adults $20. The total number of people entering the park is 217. So, one equation represents the total fees collected, and the other equation represents the total number of people. Hence, we can solve for X and Y to determine the number of children and adults admitted.