Please show an explanation

Step-by-step explanation:

1) Let x be the number of adults and y be the number of students

x + y = 8 (I)

        y = 8 -x

7.25x + 5.50y = 52.75 (II)

Substitute y = 8 -x in equation (II)

7.25x + 5.5*(8 - x) = 52.75

7.25x + 5.5*8 - x*5.5 = 52.75

7.25x +  44 - 5.5x = 52.75

7.25x - 5.5x + 44 = 52.75

             1.75x + 44 = 52.75

                  1.75x    = 52.75 - 44

                       1.75x = 8.75

                           x = 8.75/1.75

x = 5

Plugin x = 5 in equation 1

y = 8 - 5

y = 3

2)  x = y + 24

x + y = 180   {Supplementary}

y + 24 + y = 180

2y + 24 = 180

      2y = 180 - 24

     2y =  156

        y = 156/2

y = 78

x = 78 + 24 = 102

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step-by-step explanation: