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? ...

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.  

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durbanville's profile pic

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

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. 

llltkl's profile pic

llltkl | College Teacher | (Level 3) Valedictorian

Posted on

Let the number of child tickets sold be `x` .

So, the number of adult tickets sold =`(260-x)` .

Total price of the child ticket=`$ 4x`

Total price of the adult ticket=`$ 6.50(260-x)`

According to the given problem:

`4x+6.50(260-x)=1227.50`

`rArr 4x+1690-6.50x=1227.50`

`rArr 2.50x=462.50`

`rArr x=185`

So, number of child tickets sold=185

Hence, number of adult tickets sold=260-185=75

Therefore, 185 child tickets and 75 adult tickets were sold.

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