30% of the tickets sold by a movie theater for the Friday night show were children's tickets at $4 each. the rest of the tickets were sold at the full price of $8.50.the movie theater collected $360 just for the children's tickets. how many tickets did they sell in all?
360/4 = 90 children's tickets
0.3x = 90
x = 90 / 0.3
x = 300
To find the total number of tickets sold, we need to determine the number of children's tickets and the number of full-price tickets sold.
Let's start by finding the total revenue generated from children's tickets. We know that the movie theater collected $360 for the children's tickets, and each children's ticket is priced at $4. So, to find the number of children's tickets sold, we can divide the total revenue by the price of each ticket:
Number of children's tickets sold = Total revenue from children's tickets / Price of each children's ticket
Number of children's tickets sold = $360 / $4 = 90
Now, we can find the number of full-price tickets sold. To do this, we need to subtract the number of children's tickets sold from the total number of tickets sold:
Number of full-price tickets sold = Total number of tickets sold - Number of children's tickets sold
Since we don't have the total number of tickets sold yet, we'll assign it the variable "X":
Number of full-price tickets sold = X - 90
We also know that the remaining tickets were sold at the full price of $8.50. So, we can calculate the revenue generated from the full-price tickets:
Revenue from full-price tickets = Price of each full-price ticket * Number of full-price tickets sold
Revenue from full-price tickets = $8.50 * (X - 90)
The total revenue collected is given as $360. Therefore, the sum of the revenue generated from the children's tickets and the revenue generated from the full-price tickets should equal $360:
Total revenue = Revenue from children's tickets + Revenue from full-price tickets
$360 = $360 + $8.50 * (X - 90)
Now, let's solve for X:
$360 = $360 + $8.50 * (X - 90)
Subtracting $360 from both sides:
0 = $8.50 * (X - 90)
Dividing both sides by $8.50:
0/$8.50 = X - 90
0 = X - 90
Adding 90 to both sides:
90 = X
Therefore, the total number of tickets sold is 90.