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

The person below is right but they just explained it alittle oddly so I'll clarify for them because it is correct :)

y<5x+30/x

y>6x+25/x

Explanation:

Answer 2

Let
`x` be the number of movies,
`m(x)` be how much Movie Mania charges and
`t(x)` be how much Movie Time charges and
`a(x)` be Anna's plan.

Movie Mania charges a subscription fee of $30 and an additional $5 per movie


`m(x)=30+5x`

Movie Time charges a subscription fee of $25 and an additional $6 per movie


`t(x)=25+6x`

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?

That's


`t(y) < a(y) < m(y)`

Expanding it out,


`25+6y< a(y) < 30+5y`

Is there any room there?


`25+6y < 30+5y`


`y < 5`

There's no possible plan that will do what Anna wants for 5 or more movies, because in that domain Movie Time costs more than Movie Mania. She can squeeze in there between 1 and 4 movies.

I write the answer as:


`25+6y< a(y) < 30+5y`