A movie theater charges $6 for each adult and $3 for each child. If the total amount
in ticket revenue one evening was $1428 and if there were 56 more children than adults,
then how many children attended?
To solve this problem, we can use a system of equations. Let's denote the number of adults attending the movie as "a" and the number of children attending as "c".
From the information provided, we have two equations:
1. The total amount in ticket revenue is $1428:
6a + 3c = 1428
2. There were 56 more children than adults:
c = a + 56
We can solve this system by substituting equation 2 into equation 1.
6a + 3(a + 56) = 1428
Now, let's simplify and solve for "a".
6a + 3a + 168 = 1428
9a = 1428 - 168
9a = 1260
a = 1260 / 9
a = 140
So, the number of adults attending the movie is 140.
Now, let's substitute this value back into equation 2 to find the number of children attending.
c = 140 + 56
c = 196
Therefore, there were 196 children attending the movie.
C=A-56
6A+3C=1428