For a matinee movie, a total of 260 tickets were sold.  Ticket prices were $4.00/child, $6.50/adult.  There was a total of $1227.50 in ticket revenue.  How many tickets of each were sold?  Enter two numbers.  

Expert Answers

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You need to make two equations so that you can solve for both unknowns.Let x = children's tickets and Let y = adults tickets. We know there are 260 tickets altogether.

`therefore x+y=260`

Now working with the cost, we know that children's tickets cost $4 therefore we have 4x and...

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You need to make two equations so that you can solve for both unknowns.Let x = children's tickets and Let y = adults tickets. We know there are 260 tickets altogether.

`therefore x+y=260`

Now working with the cost, we know that children's tickets cost $4 therefore we have 4x and adults cost $6.50 so we have 6.5y with a total cost of $1227.50

`therefore 4x+6.5y=1227.50`

Now we can substitute to find the first unknown. You can solve for x or y first. We will solve for x, so taking the first equation we get 

`x=260-y` which we substitute into the other equation:

`therefore 4(260-y)+6.5y=1227.50`

`therefore 1040-4y+6.5y=1227.50`

`therefore 2.5y=187.50`

`therefore y=75`

As y is the number of adults tickets, then that means there are 185 (260-75) tickets in teh children's category.

Ans:

185 children's tickets are sold and 75 adults' tickets. 

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