Question

A movie theater has a membership program, $30 enrollment fee and $5 per movie. Non-members pay $8 per movie. After how many movies will having a membership pay off?

Answer 1

Answer:

The number of movies must be greater than 10

Step-by-step explanation:

Let

x ----> the number of movies

y ----> the total cost

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem we have

Membership

The slope is equal to

$m=\ 5\ per\ movie$

The y-intercept is equal to

$b=\ 30$  ---> enrollment fee

so

The linear equation is

$y=5x+30$ ----> equation A

Non-Members

The slope is equal to

$m=\ 8\ per\ movie$

The y-intercept is equal to

$b=0$  ---> Is a proportional relationship

so

The linear equation is

$y=8x$ ----> equation B

Solve the inequality

$5x+30 < 8x$

$5x-8x < -30$

$-3x < -30$

Divide both sides by -3

Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

so

$x> 10$

therefore

The number of movies must be greater than 10