17 adults, 13 Â students and 90 children
Step-by-step explanation:
Solving by using Equations
in order to answer his question we have to create two equations
we first need to give each group of people a variable:
adults = x
student = y
children = z
first equation is for the total price
5x + 2y + 0.10z = 120
second equation is for the total number of people :
x + y+ z = 120
- in this case substitution and elimination method can not work as there are three unknown variable not two
in order for the total amount from the ticket sales to be exactly $120 , then the number of children have to be a multiple of 10 ( eg 0.10 * 10 = 10)
therefore they will be no decimal point
through the use of probability and trial and error
number of  number of  number of   total cost
  children    adults     students    of tickets
    Â
    90      1      29      $ 72
    90      3      27      $ 78
    90      5      25      $ 84
    90      7      23      $ 90
    90      9      21      $ 96
    90      11      19      $102
    90      13      17      $108
    90      15      15      $114
    90      17      13      $120
17 adults, 13 Â students and 90 children
we can test this put in the equation :
5x + 2y + 0.10z = 120
5 (17) + 2 (13) + 0.10 (90) = 120
also the other equation can be used to check if it is correct :
x + y+ z = 120
17 + 13 + 90 = 120
hence this answer is CORRECT
