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.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: