Question

Anna plans a business model to compete with two video stores, where she hopes to draw in customers from one store but not lose money on the deal. Movie Mania charges a subscription fee of $30 and an additional $5 per movie, x. Movie Time charges a subscription fee of $25 and an additional $6 per movie, x. Based on this information, which system of inequalities could be used to determine how many movies need to be rented for a customer on Anna’s plan, y, to pay her more than they would at Movie Time, but less than they would at Movie Mania?

Answer 1

Movie Mania charges a subscription fee of $30 and an additional $5 per movie, x. So the total charges at Movie Mania for x movies will be:

30 + 5x

Movie Time charges a subscription fee of $25 and an additional $6 per movie, x. So the total charges at Movie Time for x movies will be:

25 + 6x

Anna wants her plan to her amount y which is more than Movie Time but Less than Movie Mania. So we can set up the equation as:

Cost at Movie Time < y < Cost at Movie Mania

Using the values, we can write:

25 + 6x < y < 30 + 5x

Using this system of inequalities Anna can determine how many movies need to be rented for a customer on her plan