Final answer:
The equation that represents the ticket sales for x customers at the movie theater is t(x) = 13.75x.
Step-by-step explanation:
The problem asks us to find the equation that represents the ticket sales for x customers at a movie theater. We are given that the amount of sales varies directly with the number of customers. This means that the equation should have a constant of proportionality.
Let's start by setting up the equation. We know that twenty customers paid a total of $275 for tickets. So, the total amount of ticket sales (t) is $275, and the number of customers (x) is 20.
We can set up the equation as t(x) = kx, where k is the constant of proportionality. To find the value of k, we can substitute the given values into the equation: $275 = k(20), which simplifies to 275 = 20k. Solving for k, we divide both sides by 20, giving us k = 275/20 = 13.75.
Therefore, the equation that represents the ticket sales for x customers at the movie theater is t(x) = 13.75x.