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.
What is the maximum number of people that could attend your party in order for the individual admission rate to be a better deal?
Let's assume the maximum number of people that could attend the party is 'x'.
For individual admissions, each person will pay $12.99.
For the group rate, each person will pay $8.99 plus the $20 reservation fee.
To determine for which situation the individual admission rate is a better deal, we need to compare the total cost in both scenarios.
For individual admissions:
Total cost = $12.99 * x
For the group rate:
Total cost = ($8.99 * x) + $20
To find the maximum number 'x' for which the individual admission rate is a better deal, we need to set up the following inequality:
$12.99 * x < ($8.99 * x) + $20
Simplifying the inequality:
$12.99 * x < $8.99 * x + $20
$12.99 * x - $8.99 * x < $20
$4 * x < $20
x < $20/$4
x < 5
Hence, the maximum number of people that could attend the party for the individual admission rate to be a better deal is 4 (as 5 or more people will make the group rate a better deal).