Adult tickets for a play cost $18 and child tickets cost $12. If there were 20 people at a performance and the theatre collected $246 from ticket sales, how many adults and how many children attended the play?
c + a = 20 so c = 20-a
12 c + 18 a = 246
12(20-a) + 18 a = 246
240 -12 a + 18 a = 246 etc
x = adults
20 - x = children
18(x) + 12(20-x) = 246
12x + 240 - 12x = 246
Simplify: 6x = 6
So x = 1 adult
20 - 1 = 19 children :)
To solve this problem, let's assign variables to the unknowns:
Let A be the number of adults and C be the number of children.
We know that the adult tickets cost $18 and the child tickets cost $12.
There were a total of 20 people at the performance, so we can write the equation A + C = 20 (Equation 1).
The total amount collected from ticket sales is $246, which means that the sum of all the adult ticket prices and the sum of all the child ticket prices must equal $246.
The sum of the adult ticket prices is 18A, and the sum of the child ticket prices is 12C.
So we can write the equation 18A + 12C = 246 (Equation 2).
Now we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of A and C.
One way to do this is by substituting the value of A from Equation 1 into Equation 2.
Let's solve Equation 1 for A:
A = 20 - C.
Now we substitute this value of A into Equation 2:
18(20 - C) + 12C = 246.
Let's simplify this equation:
360 - 18C + 12C = 246.
Combine like terms:
-6C + 360 = 246.
Subtract 360 from both sides:
-6C = -114.
Divide both sides by -6:
C = 19.
Now we know that there were 19 children.
To find the number of adults, substitute the value of C into Equation 1:
A = 20 - 19 = 1.
Therefore, there was 1 adult and 19 children who attended the play.