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
[tex]y=mx+b[/tex]
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
[tex]m=\$5\ per\ movie[/tex]
The y-intercept is equal to
[tex]b=\$30[/tex] ---> enrollment fee
so
The linear equation is
[tex]y=5x+30[/tex] ----> equation A
Non-Members
The slope is equal to
[tex]m=\$8\ per\ movie[/tex]
The y-intercept is equal to
[tex]b=0[/tex] ---> Is a proportional relationship
so
The linear equation is
[tex]y=8x[/tex] ----> equation B
Solve the inequality
[tex]5x+30 < 8x[/tex]
[tex]5x-8x < -30[/tex]
[tex]-3x < -30[/tex]
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
[tex]x> 10[/tex]
therefore
The number of movies must be greater than 10
