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?
x total tickets sold
.3x tickets sold as childrens
.3x(4) = 360
1.2x = 360
x =300
To find the total number of tickets sold, we need to determine the number of children's tickets and the number of adult tickets. We have been given that 30% of the tickets sold were children's tickets.
Let's assume the total number of tickets sold is "x". Since 30% of the tickets were children's tickets, we can calculate the number of children's tickets by multiplying 30% by the total number of tickets sold:
Number of children's tickets = 30% of x = 0.3 * x
We also know that the cost of each children's ticket is $4 and the movie theater collected $360 just for the children's tickets. Therefore, we can write the following equation:
0.3 * x * $4 = $360
To solve for x, we can divide both sides of the equation by $4 and then divide by 0.3:
0.3 * x * $4 / $4 = $360 / $4 / 0.3
0.3 * x = $360 / $4 / 0.3
Simplifying further:
0.3 * x = $360 / 12
0.3 * x = $30
Dividing both sides by 0.3:
x = $30 / 0.3
x = $100
Therefore, the total number of tickets sold by the movie theater for the Friday night show was 100.