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A movie theater has a seating capacity of 233. 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 $ 1692, How many children, students, and adults attended? I kinda need to know these answers asap. I have tried everything to try and solve it but nothing worked. Please help.

Respuesta :

skylart924

Answer:

49 adults;  2*49 = 98 children  and  (207-3*49) = 60 students.

Step-by-step explanation:

hope this helps!! :))

varshamittal029

122 children, 50 students, and 122 adults attended the movie theatre.

What is an equation?

A mathematical expression with an equality sign between two mathematical expressions is an equation.

How to solve it?

Let the number of students in the theater = x and the number of children in the theater = 2y

Since the number of adults in theater = Half of the number of children = 2y/2 = y

Given that the total seating capacity in the theater = 233

So, we can write

x  + 2y + y =  233

i.e.  x + 3y = 233 ...(1)

Given that the cost of 1 children's ticket = $5

i.e. the cost of 2y children tickets = 5 x (2y) = $10y

The cost of 1 student ticket = $7

i.e. the cost of x student ticket = $7x

The cost of 1 adult ticket = $12

i.e. the cost of y adult tickets = $12y  

Since the total ticket sales was $1692,

So, we can write

10y  + 7x + 12y =  1692

i.e. 7x + 22y = 1692 ...(2)

Now we have to solve the two equations (1) and (2).

multiplying (1) by 7,

7x + 21y = 1631 ...(3)

Subtracting (3) from (2),

7x + 22y - 7x - 21y = 1692 - 1631

i.e. y = 61

then 2y = 122

and x = 233 - (3 x 61) = 233 - 183 = 50

Therefore 122 children, 50 students, and 122 adults attended the movie theatre.

Learn more about the equations here -

https://brainly.com/question/13980943

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