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You are planning to take a group of friends to the movies for your birthday. The local movie theater charges $12.99 per person. When you check the company's website, you find that they also offer a special group rate. The group rate is only $8.99 per person but also includes a $20 reservation fee in addition to the cost per person

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badddiee
The green line represents the group rate at the movie theater. The blue line represents the individual rate. The two lines intersect at the point (5, 64.95), which represents that the price for 5 people is the same for both the individual rate and the group rate. For fewer than 5 people, the individual admission rate line is below the group rate line. The maximum number of people who can attend the party and have the individual admission rate to be a better deal is 4 people. 
facundo3141592

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.

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