Multiple Choice 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
Let C be the number of children's tickets sold and A be the number of adult tickets sold.
We know that C + A = 233 and 8C + 12A = 2156.
From the first equation, we can solve for A in terms of C: A = 233 - C.
Substituting this into the second equation, we get 8C + 12(233 - C) = 2156.
Expanding and simplifying the equation, we get 8C + 2796 - 12C = 2156.
Combining like terms, we get -4C + 2796 = 2156.
Subtracting 2796 from both sides, we get -4C = -640.
Dividing both sides by -4, we get C = 160.
Therefore, 160 children's tickets were sold.
The answer is C. 160.