SOLUTION: Adult tickets for a play cost $18 and child tickets cost $2. If there were 20 people at a performance and the theater collected $88 from ticket sales, how many children attended t

Click here to see ALL problems on Miscellaneous Word Problems

Question 106455: Adult tickets for a play cost $18 and child tickets cost $2. If there were 20 people at a performance and the theater collected $88 from ticket sales, how many children attended the play?
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!
Let's say the number of adults is 'a' and that the number of children is 'c'

Since all 20 of the people who attended were either adults or children, we can say:

Eq 1)

Since each adult paid $18, the amount of money collected from all the adults must be 18a. Similarly, the amount of money collected from all the children must be 2c. Since the total amount of money is $88 and all of the money either came from adults or children we know that:

Eq 2)

Rearranging Eq 1, we find that

Substituting this value for 'c' into Eq 2 yields

Simplifying and solving:

Hence, there were 3 adults in the audience, and therefore 20-3 or 17 children.

Let's check:
$18 X 3 = $54
$2 X 17 = $34
$54 + $34 = $88 Check!