Admission for a movie is $8 for children and $12 for adults. On a certain day, 3200 people attend the movie theater and $33,040 is collected.

How many children and how many adults attended the movies?

children

adults

Let us assume the number of children attending the movie = x

Let us also assume the number of adults attending the movie = y

Cost of admission for a children in the movie = $8

Cost of admission of an adult in the movie = $12

Number of people going to the movie on a certain day = 3200

Total amount collected from the movie theater = $33040

Then

x + y = 3200

And

8x + 12y = 33040

2x + 3y = 8260

Let us first take the equation

x + y = 3200

x = 3200 - y

Now we will put the value of x in the equation

2x + 3y = 8260

2 (3200 - y) + 3y = 8260

6400 - 2y + 3y = 8260

y = 8260 - 6400

= 1860

Now we will put the value of y from the above deduction in the equation

x + y = 3200

x + 1860 = 3200

x = 3200 - 1860

= 1340

So the number of children going to the movie theater is 1340 and the number of adults going to the movie theater is 1860.