A movie theater charges $6 for an adult and $3 for a child. if the total amount was 1428 and there were 56 more children than adults - then how many children attended?
Is 1428 attendance or amount of money taken in?
If money:
Let x = children, then x - 56 = adults
3x + 6(x-56) = 1428
Calculate for x.
196
smd
To find the number of children who attended the movie theater, we can set up a system of equations based on the given information.
Let's assume the number of adults attending the movie theater is represented by 'A' and the number of children attending is represented by 'C'.
According to the given information, the movie theater charges $6 per adult, so the total revenue from adults can be calculated by multiplying the number of adults by the ticket price: 6 * A.
Similarly, the movie theater charges $3 per child, so the total revenue from children can be calculated by multiplying the number of children by the ticket price: 3 * C.
The total amount collected from admissions is $1428, so we have the equation: 6A + 3C = 1428.
We are also given that the number of children attending is 56 more than the number of adults: C = A + 56.
Now we can solve this system of equations to find the values of A and C.
1. Substitute the expression for C from the second equation into the first equation:
6A + 3(A + 56) = 1428.
2. Simplify and solve for A:
6A + 3A + 168 = 1428,
9A = 1428 - 168,
9A = 1260,
A = 1260 / 9,
A = 140.
We have found that the number of adults (A) attending the movie theater is 140.
3. Substitute the value of A into the second equation:
C = 140 + 56,
C = 196.
Thus, the number of children (C) who attended the movie theater is 196.