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

From the problem, we can set up the following equations based on the information given:

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

2. The total revenue from the tickets sold:
\[
8x + 12y = 2156
\]

Now we have a system of equations to solve.

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

Next, we will substitute this expression for \( y \) into the second equation:
\[
8x + 12(233 - x) = 2156
\]

Now distribute the 12:
\[
8x + 2796 - 12x = 2156
\]

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

Now, subtract 2796 from both sides:
\[
-4x = 2156 - 2796
\]
\[
-4x = -640
\]

Now divide by -4:
\[
x = 160
\]

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

To confirm our solution, we can find \( y \) using \( y = 233 - x \):
\[
y = 233 - 160 = 73
\]

Now, we can check the revenue:
\[
8x + 12y = 8(160) + 12(73) = 1280 + 876 = 2156
\]
The revenue checks out, confirming that the solution is correct. The number of children’s tickets sold is indeed \( \boxed{160} \).