a movie theater charges $9 for an adults ticket and $5.00 for a child ticket. on a recent night the sale of child's tickets was two times the sale of an adults tickets. if the total amount collected for ticket sales was not more than $3800 what is the greatest number of adults who could have purchase tickets.
If x = adult tickets, then 2x = children's tickets
9x + 5(2x) < 3800
Solve for x.
200
I have almost the same question except for different numbers, do you think you can help me with it?
To find the greatest number of adults who could have purchased tickets, we need to set up and solve an equation based on the given information.
Let's assume the number of adult tickets sold is "x". Since the sale of children's tickets was two times the sale of adult tickets, the number of children's tickets sold would be 2x.
To determine the total amount collected for ticket sales, we multiply the price of each adult ticket by the number of adult tickets sold, and the price of each child ticket by the number of child tickets sold:
Total amount collected = (Price of adult ticket * Number of adult tickets sold) + (Price of child ticket * Number of child tickets sold)
Total amount collected = (9 * x) + (5 * 2x)
We know that the total amount collected is not more than $3800, so we can write:
(9 * x) + (5 * 2x) ≤ 3800
Simplifying the equation:
9x + 10x ≤ 3800
19x ≤ 3800
x ≤ 200
Therefore, the greatest number of adults who could have purchased tickets is 200.