A movie theater has a seating capacity of 315. 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 $ 2280, How many children, students, and adults attended?

84 students

Step-by-step explanation:

Let x be the number of adults.

Then the number of children is 2x, according to the condition,

and the number of students is the rest (315-x-2x) = (315-3x).

The "money" equation (the revenue equation) is

12x + 5x (2x) + 7x (315-3x) = 2282.

12x + 10x + 7x315 - 21x = 2282

x = 2282 - 7x315 = 77 is the number of adults.

77 adults : 2 x 77 = 154 children and the rest (315-77-154) = 84 students.