A theater contains 441 seats and the ticket prices for a recent play were $45 for adults and $21 for children. if the total proceeds were 13,797 for a sold out matinee, how many of each type of ticket were sold?.
a = Number of adults
c = Number of children
Total numbers of spectator = 441
a + c = 441
Total proceeds = 13,797 $
a * 45 $ + c * 21 $ = 13,797 $
Now you must solve system of two equation :
a + c = 441
45 a + 21 c = 13,797
Try it.
The solutions are :
a = 189
c = 252
Proof :
a * 45 $ + c * 21 $ =
189 * 45 $ + 252 * 21 $ =
8,505 $ + 5,292 $ = 13,797 $
WHY DO YOU PUT THE DOLLAR SIGN AFTER THE MONEY... THATS DUMB
To solve this problem, we can use a system of equations. Let's assume the number of adult tickets sold is represented by 'A', and the number of children's tickets sold is represented by 'C'.
According to the problem, the total number of tickets sold was equal to the seating capacity of 441:
A + C = 441 ...(Equation 1)
The total proceeds from the tickets sold are given as $13,797:
45A + 21C = 13,797 ...(Equation 2)
Now we have two equations with two variables. We can use either substitution or elimination method to solve this system of equations.
Let's use the elimination method.
Multiply Equation 1 by 45 (to match the coefficient of 'A'):
45A + 45C = 19845 ...(Equation 3)
Now subtract Equation 2 from Equation 3 (to eliminate 'A'):
(45A + 45C) - (45A + 21C) = 19845 - 13797
45C - 21C = 6051
Simplifying further, we get:
24C = 6051
Divide both sides by 24:
C = 6051 / 24
C ≈ 252.125
Since the number of children's tickets cannot be a decimal, we need to round down to the nearest whole number:
C ≈ 252
Now substitute this value back into Equation 1 to find the number of adult tickets:
A + 252 = 441
A = 441 - 252
A = 189
So, approximately 189 adult tickets and 252 children's tickets were sold for the matinee.