Question

The County Carnival is calculating attendance for the end of the first week. They sell adult tickets for $15 and children's tickets for $8. 70% of the tickets sold were children's tickets. 4600 less adult tickets were sold than children's tickets. How many of each type of ticket was sold the first week? How much money was made from the sale of children's tickets?

Set up a proportional equation that represents the scenario.
Show all your work.

Answer 1

8050 children's tickets

3450 adult's tickets

Children's tickets sales = $64,400

Explanation:

a = number of adult's tickets sold

c = number of children's tickets sold

1. Since 70% of the tickets were children's, 30% were adult's:

`(70)/(30)=(c)/(a)` ⇒
`(7)/(3)=(c)/(a)`

2. "4600 less adult tickets were sold than children's tickets":

a = c - 4600

3. Substitute:

`(7)/(3)=(c)/(c-4600)`

4. Solve for c:

7(c-4600) = 3c

7c - 32200 = 3c

4c = 32200

c = 8050 = number of children's tickets sold

5. Calculate the number of adult's tickets sold:

a = c - 4600

= 8050 - 4600

a = 3450

6. Money made from sale of children's tickets = 8c = 8(8050) = 64,400