Answer:
The expression that represents the profit per ticket is:
C) x (10x - 450)
In this expression, x represents the number of tickets sold, and (10x - 450) represents the total profit obtained by selling those tickets. By dividing the total profit by the number of tickets sold (x), we get the profit per ticket.
Explanation:
Let's break down the expression and its components to understand why C) x (10x - 450) represents the profit per ticket.
The given expression for profit is 10x - 450, where x represents the number of tickets sold. This expression calculates the total profit made from selling x tickets by subtracting the total cost ($450) from the total revenue generated (10x).
To find the profit per ticket, we divide the total profit by the number of tickets sold. Dividing the expression 10x - 450 by x gives us (10x - 450) / x. However, option B) (10x - 450) / z, where z ≠ 0, is not the correct representation of the profit per ticket because it introduces an additional variable, z, which is not relevant to the problem.
Option C) x (10x - 450) correctly represents the profit per ticket. Multiplying x by (10x - 450) means multiplying the number of tickets sold by the profit earned from each ticket. This expression gives us the total profit obtained from x tickets, which can then be divided by x to find the profit per ticket.
For example, if we sold 100 tickets (x = 100), the expression x (10x - 450) would give us 100 * (10 * 100 - 450) = 100 * (1000 - 450) = 100 * 550 = 55,000. Dividing this total profit of 55,000 by the number of tickets sold (100) gives us 550, which represents the profit per ticket.
Therefore, the correct expression for the profit per ticket is C) x (10x - 450), where x represents the number of tickets sold.