The admission fee at a fair is $3.25 for children and $6.75 for adults. on a certain day, 870 people enter the fair and $3,772.50 is collected. write a system of linear equations that you can use to determine how many children and adults attended. be sure to define your variables. solve the system. show your work !

       Total number of children = 600

        Total number of adults = 270

Explanation:

 Admission fee at fair for children = $3.25

 Admission fee at fair for adults = $6.75

 Total people entered the fair = 870

 Collected amount = $3,772.50

 Let X be the number of children and Y be the number of adults.

 We have total of 870 people

     X + Y = 870   Equation 1

Collected amount = $3,772.50

  3.25 X + 6.75 Y = 3,772.50Equation 2

 Multiplying equation 1 with 3.25,

    3.25 X + 3.25 Y = 2827.5Equation 3

Equation 2 - Equation 3,

     (3.25 X + 6.75 Y) - ( 3.25 X + 3.25 Y) = 3,772.50 - 2827.5

           3.5 Y = 945

              Y = 270 adults.

    Substituting in equation 1

         X + 270 = 870

          X = 600 children.

  So Total number of children = 600

        Total number of adults = 270