Question

$ 9099 worth of tickets are sold. Adult tickets are $8 a person. Students are $6 a person. Children are $5 a person. 102 more adult ticket are sold than students tickets. Two times more student tickets are sold than children tickets. How many children tickets were sold

Answer 1

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