Question 103089: Adult tickets for a play cost $13 and child tickets cost $1. If there were 22 people at a performance and the theater collected $58 from ticket sales, how many adults and how many children attended the play?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! This type of problem is generally a "mixture" problem. You need to find the "mix" of adult and child tickets that totals some dollar value, given there were n people in the audience.
Let's start by declaring x the variable for adult tickets. Since there 22 tickets sold, then there had to be 22-x child tickets.
Adult tickets sell for $13, so 13x = revenue from adult tickets
Child tickets sell for $1, so 1*(22-x) or simply 22-x = the revenue from child tickets.
The total revenue was $58, which includes adult and child ticket sales.
So, 13x + (22-x) = 58.
Removing the parenthesis and combining the x terms on the left:
12x + 22 = 58
Subtracting 22 from both sides:
12x = 36
Dividing through by 12:
x = 3
So there 3 adult tickets sold, which generates $39 revenue.
There were 22-3 = 19 child tickets sold for $1 each, or $19 revenue.
$39 + $19 = $58. Which confirms the answer.
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