Question

Tickets for a carnival cost $8 for children age 12 and under and $12 for anyone over 12 years of age. The carnival sold a total of 233 tickets and collected $2,156. How many children’s tickets were sold?

A.
73

B.
108

C.
160

D.
180

Answer 1

Let \( x \) be the number of children's tickets sold and \( y \) be the number of adult tickets sold.

We have the following equations based on the problem statement:

1. The equation for the total number of tickets sold:
\[
x + y = 233
\]

2. The equation for the total revenue collected from ticket sales:
\[
8x + 12y = 2156
\]

Now we can solve these equations step by step.

First, solve the first equation for \( y \):
\[
y = 233 - x
\]

Now substitute \( y \) in the second equation:
\[
8x + 12(233 - x) = 2156
\]

Expanding that, we get:
\[
8x + 2796 - 12x = 2156
\]

Combine like terms:
\[
-4x + 2796 = 2156
\]

Now, isolate \( x \):
\[
-4x = 2156 - 2796
\]
\[
-4x = -640
\]
\[
x = \frac{-640}{-4} = 160
\]

So, the number of children's tickets sold is \( \boxed{160} \).

To verify, we can find \( y \):
\[
y = 233 - 160 = 73
\]

Now, check the revenue:
\[
8(160) + 12(73) = 1280 + 876 = 2156
\]

Both conditions are satisfied, confirming that the number of children's tickets sold is indeed \( \boxed{160} \).