A movie theater charges $11 for each adult and $6 for each ticket. one day, they sold 163 tickets and made $1578. How many of each ticket did they sell?

a+c = 163

11a+6c = 1578

To solve this problem, we can use a system of equations. Let's denote the number of adult tickets sold as 'a' and the number of child tickets sold as 'c'.

Given that the movie theater sold a total of 163 tickets, we can write the equation:
a + c = 163 (Equation 1)

Since each adult ticket costs $11 and each child ticket costs $6, we can write the equation for the total revenue generated:
11a + 6c = 1578 (Equation 2)

Now, we have a system of two equations with two unknowns:
a + c = 163 (Equation 1)
11a + 6c = 1578 (Equation 2)

We can solve this system of equations using substitution or elimination method. Let's use substitution:

From Equation 1, we can isolate 'a', which gives us:
a = 163 - c

Substituting this value of 'a' into Equation 2, we get:
11(163 - c) + 6c = 1578
1793 - 11c + 6c = 1578
-5c = 1578 - 1793
-5c = -215

Dividing both sides by -5, we find:
c = (-215) / (-5) = 43

Now, substitute the value of 'c' back into Equation 1:
a + 43 = 163
a = 163 - 43
a = 120

Therefore, the movie theater sold 120 adult tickets (a) and 43 child tickets (c).