Answer: Hello mate!
lets suppose you have (x -1) friends (then when you count yourself, there are x persons in the group) where x is a natural number.
you have two possible prices at the movie theater:
1) the $12.99 per person, then if you have x persons in the group, the total charge is $12.99*x
2) with the promotion they pay $8.99 per person and includes a $20 reservation, then the total charge is $8.99*x + $20
now, let's find the number x is where the second option is cheaper than the first.
in order to do this, we can regulate both equations in order to determine in which x₀ the costs are the same, then if x< x₀, the first option is cheaper and if x>x₀ the second option is cheaper.
$12.99*x₀ = $20 + $8.99x₀
$12.99x₀ - $8.99x₀ = $20
$4x₀ = $20
x₀ = 20/4 = 5
Then if in your group are less than 5 persons, took option 1.
if there are more than 5 persons, took the option 2
if there are exactly 5 persons, both options cost the same.