A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for stu

A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1030, How many children, students, and adults attended?

Let c be the number of children's tickets, s be the number of student's tickets, and a be the number of adult's tickets. We have 3 equations:

1. a + c + s = 143
2. a = 0.5c
3. 12a + 5c + 7s =1030

Substitute (2) into (1)
0.5c + c + s = 143
1.5c + s = 143

Subtract 1.5c from each side
4. s = 143 - 1.5c

Now, take (4) and (2), and plug it into (3)
12(0.5c) + 5c + 7(143 - 1.5c) = 1030
6c + 5c + 1001 - 10.5c = 1030

Combine like terms:
0.5c + 1001 = 1030

Use our equation calculator to get c = 58.

Plug this back into (2)
a = 0.5(58)
a = 29

Now take the a and c values, and plug it into (1)
29 + 58 + s = 143
s + 87 = 143

Using our equation calculator again, we get s = 56.

To summarize, we have:

• 29 adults
• 58 children
• 56 students