A total of 500 tickets were sold for a game for a total of $1940. If adult tickets sold for $7 each and child tickets cost $1 each, how many of each kind of ticket were sold?

Question

A total of 500 tickets were sold for a game for a total of $1940. If adult tickets sold for $7 each and child tickets cost $1 each, how many of each kind of ticket were sold?

adults Tickets =

Child Tickets=

Answer 1

With the information given we can generate two equations:

Let x be the number of adult tickets sold.

Let y be the number of child tickets sold.

Because we know that we sold 500 tickets total, x + y should equal our total, hence:

x + y = 500

For the second equation, we know that we have a total price of $1940. Since x is the number of adult tickets sold, then 7x will be the dollar amount of adult tickets sold. Likewise, y is the number of child tickets sold, but they're only worth $1 so we just leave it as y (if the child tickets were $2 we would represent this by 2y). Hence our equation for the total dollar amount is:

7x + y = 1940

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We have to eliminate one of the variables in order to solve this system of equations, so line them up like this:

7x + y = 1940

x + y = 500

Now subtract the second equation from the first equation:

(7x-x) + (y-y) = 1940 - 500

6x = 1440

x = 240

To find the number of child tickets, plug in this x into either equation:

(240) + y = 500

y = 260

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# of adult tickets: 240

# of child tickets: 260

Always plug in your x and y values into both equations to verify that the answers are correct!

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