a movie theater charges $7 for an adult's ticket and $4 for a child's ticket.
on a recent night the sale of child's tickets was three times the sale of adult's tickets.
if the total anount collected for ticket sales was not more than $2,000,
what is the greatest number of adults who could hace prtchased tickets?
[ show or explain the procedure used to obtain your answer.]
child's ticket is 316
adult's ticket is 105
105:))))))))
To find the greatest number of adults who could have purchased tickets, we can use a systematic approach by setting up equations based on the given information.
Let's start with defining some variables:
Let's say the number of adult's tickets sold is "a."
And the number of child's tickets sold is "c."
According to the given information:
The cost of each adult's ticket is $7, so the total amount collected from adult's tickets is 7a.
The cost of each child's ticket is $4, so the total amount collected from child's tickets is 4c.
The problem states that the sale of child's tickets was three times the sale of adult's tickets:
c = 3a
The total amount collected for ticket sales was not more than $2,000:
7a + 4c ≤ 2000
Now, let's substitute the value of "c" from the first equation into the second equation:
7a + 4(3a) ≤ 2000
7a + 12a ≤ 2000
19a ≤ 2000
a ≤ 2000/19
To find the greatest number of adults who could have purchased tickets, we need to find the largest whole number value of "a" that satisfies this inequality.
Dividing 2000 by 19 gives us approximately 105.26. Since we need to find the largest whole number value, we take the largest integer value less than or equal to 105.26, which is 105.
Therefore, the greatest number of adults who could have purchased tickets is 105.