Adult tickets for a play cost $15 and child tickets cost $6. If there were 33 people at a performance and the theater collected $360 from ticket sales, how many children attended the play?
14 children
15 children
16 children
18 children
let the number of kids at the show be x
then number of adults is 33-x
6x + 15(33-x) = 360
etc
To find the number of children who attended the play, we need to set up equations based on the information given.
Let's assume that the number of adults who attended the play is "x" and the number of children who attended the play is "y".
According to the given information, the total number of people who attended the play is 33. So we can write the equation:
x + y = 33 ---(1)
We also know that the cost of an adult ticket is $15 and the cost of a child ticket is $6. The theater collected a total of $360 from ticket sales. The amount collected from adult tickets can be calculated as:
Adult tickets = x * $15
Similarly, the amount collected from child tickets can be calculated as:
Child tickets = y * $6
According to the given information, the total ticket sales amount is $360. So we can write the equation:
Adult tickets + Child tickets = $360
(x * $15) + (y * $6) = $360 ---(2)
Now we have two equations:
x + y = 33 ---(1)
(x * $15) + (y * $6) = $360 ---(2)
We can solve these equations to find the values of x and y, which represent the number of adults and children who attended the play, respectively.
To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method to solve it:
Multiplying equation (1) by $6, we get:
6x + 6y = $198 ---(3)
Now, subtract equation (3) from equation (2):
[(x * $15) + (y * $6)] - (6x + 6y) = $360 - $198
Simplifying:
15x - 6x + 6y - 6y = $162
9x = $162
Dividing both sides by 9, we get:
x = $162 / 9
x = 18
So, the number of adults who attended the play is 18.
Substituting the value of x in equation (1):
18 + y = 33
Subtracting 18 from both sides, we get:
y = 33 - 18
y = 15
So, the number of children who attended the play is 15.
Therefore, the correct answer is: 15 children.