SOLUTION: Adult tickets for a play cost $20 and child tickets cost $8. If there were 33 people at a performance and the theater collected $468 from ticket sales, how many adults and how man

Question 71898: Adult tickets for a play cost $20 and child tickets cost $8. If there were 33 people at a performance and the theater collected $468 from ticket sales, how many adults and how many children attended the play?
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
Let the no. of adults and children who attended be 'x' and 'y' respectively.

Cost of each adult ticket = $20.
Cost of all adult tickets when 'x' adults were present = $(20x).

Cost of each children ticket = $8.
Cost of all children tickets when 'y' children were present = $(8y).

Hence the total cost of children's and adults' tickets = $(20x + 8y).
This value is given as $468.

So, 20x + 8y = 468 or 5x + 2y = 117. This is one equation.

Again, total no. of adults and children = (x + y).
This value is given to be 33.

So, x + y = 33. This is the other equation.

Now we have to solve 2 equations.
5x + 2y = 117 __________(1)
x + y = 33 ___________(2)

Multiplying equation (2) by 2 and then subtracting from equation (1)

So, y
= 33 - x [Recall eqn. (1) which says x + y =33]
= 33 - 17
= 16

So there were x = 17 adults and y = 16 children.
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