A particular movie theater charges per adult and per child. If people attended a movie and the total revenue from ticket sales was , which of the following models the given information if represents the number of adults and represents the number of children?
The correct answer and explanation is:
To model the total revenue from ticket sales based on the number of adults and children, we can break the problem into two components:
- Cost per Adult Ticket (Let’s say AA): This is the amount charged for one adult ticket. If there are xx adults attending the movie, the total revenue from adult tickets would be A⋅xA \cdot x.
- Cost per Child Ticket (Let’s say CC): This is the amount charged for one child ticket. If there are yy children attending the movie, the total revenue from child tickets would be C⋅yC \cdot y.
Now, to find the total revenue, we sum the revenue from both adults and children: Total Revenue=(A⋅x)+(C⋅y)\text{Total Revenue} = (A \cdot x) + (C \cdot y)
In this equation:
- xx represents the number of adults.
- yy represents the number of children.
- AA represents the cost of an adult ticket.
- CC represents the cost of a child ticket.
So, the correct model to represent the total revenue is: Total Revenue=A⋅x+C⋅y\text{Total Revenue} = A \cdot x + C \cdot y
This equation tells you how the total revenue is determined by multiplying the number of adults by the price of the adult ticket and the number of children by the price of the child ticket. The sum of both these values gives the total revenue from ticket sales.
This model can be used to predict the revenue based on the number of people attending the movie, as long as the prices per ticket for adults and children are known. It provides a linear relationship between the total number of tickets sold and the revenue, making it straightforward to calculate the theater’s income based on varying attendance.