Answer:
The Answer is: There were 604 adult tickets sold and 502 student tickets sold and 251 children tickets sold.
Explanation:
Let a = the number of adult tickets. Let s = the number of student tickets. Let c = the number of children tickets sold. The total of all tickets sold is equal to $9,099. Equation below:
8a + 6s + 5c = $9,099
There are 102 more adult tickets than students. Equation below:
a = s + 102
There are twice as many student tickets than children tickets. Equation below:
c = s/2
By substitution, solve the equation:
8a + 6s + 5c = $9,099
8(s + 102) + 6s + 5(s/2) = 9099
8s + 816 + 6s + 5s/2 = 9099
14s + 5s/2 = 9099 - 816
14s + 5s/2 = 8283
28s + 5s = 16566
33s = 16566
s = 502 student tickets.
Solve for a:
a = s + 102 = 502 + 102 = 604 adult tickets.
Solve for c:
c = s/2 = 502 / 2 = 251 children tickets.
Proof:
8(502 + 102) + 6(502) + 5(251) =
8(604) + 6(502) + 5(251) =
4832 + 3012 + 1255 = 9099
9099 = 9099