Anna plans a business model to compete with two video stores, where she hopes to draw in customers from one store but not lose m

Question

3 years ago

15

Anna plans a business model to compete with two video stores, where she hopes to draw in customers from one store but not lose m

oney 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?

Mathematics

2 answers:

babymother [125] · Answer 1 · 2022-03-09T22:24:24+03:00

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:

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