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
To solve this problem, we can set up a system of equations. Let x represent the number of children's tickets sold and y represent the number of adult tickets sold.
Given:
x + y = 233 (total number of tickets sold)
8x + 12y = 2156 (total amount collected)
Now we can solve this system of equations. We can solve the first equation for y:
y = 233 - x
Substitute this into the second equation:
8x + 12(233 - x) = 2156
8x + 2796 - 12x = 2156
-4x = -640
x = 160
Therefore, the number of children's tickets sold was 160. The answer is C. 160.