Children's tickets to a movie cost $7. Adult tickets cost $12. If 275 tickets were sold for a total of $2490.00, how many of each type were sold?

Let adult A and children C

A + C = 275
12A + 7C = 2490

Substituting

A = 275 -C

12(275- C) + 7C = 2490

3300 -12C + 7C = 2490

3300 -5C = 2490

3300-3300 -5C = 2490 - 3300

-5C = -810

C = 162

A = 113

Excellent! Thank you Kuai!

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c 162

a 113

To solve this problem, we can use a system of equations. Let's assume that the number of children's tickets sold is represented by C, and the number of adult tickets sold is represented by A.

We are given two pieces of information:
1. The cost of a children's ticket is $7: C * 7
2. The cost of an adult ticket is $12: A * 12

We also know that the total number of tickets sold is 275 and the total revenue from ticket sales is $2490.00.

So, we can set up two equations to represent the given information:
1. C + A = 275 (equation 1)
2. 7C + 12A = 2490 (equation 2)

Now we can solve this system of equations to find the values of C and A.

One way to solve this system of equations is by substitution. Rearrange equation 1 to solve for C:
C = 275 - A

Now substitute this expression for C in equation 2:
7(275 - A) + 12A = 2490

Distribute the 7:
1925 - 7A + 12A = 2490

Combine like terms:
5A = 565

Divide by 5:
A = 113

Now substitute this value of A back into equation 1 to find C:
C + 113 = 275
C = 162

Therefore, 162 children's tickets and 113 adult tickets were sold.