Final answer:
Denise bought 32 children's tickets and 40 adult tickets. We used a system of equations to find that there were 32 children's tickets at $10 each and 40 adult tickets at $22 each to total $1200 for 72 tickets.
Step-by-step explanation:
To solve the problem of how many children and adult tickets Denise bought, we can set up a system of equations based on the given information. Let's designate C as the number of children's tickets and A as the number of adult tickets.
According to the problem, we have two key pieces of information:
- The cost for children tickets is $10 each and for adults, $22 for each, leading to the equation: 10C + 22A = 1200 (1) which represents the total amount spent.
- Denise bought a total of 72 tickets, giving us the equation: C + A = 72 (2) which represents the total number of tickets.
We need to solve this system to find the values of C and A. By manipulating equation (2), we can express A as A = 72 - C and substitute it into equation (1).
Substituting A in equation (1):
10C + 22(72 - C) = 1200
Now, let's solve for C:
10C + 1584 - 22C = 1200
-12C = 1200 - 1584
-12C = -384
C = 32
Now we know there were 32 children's tickets. We can use this number to find the number of adult tickets:
A = 72 - C
A = 72 - 32
A = 40
So, Denise bought 32 children's tickets and 40 adult tickets.