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 the 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 attending the party is represented by 'n'.
For the regular admission rate, the cost per person is $12.99.
For the group rate, the cost per person is $8.99 + $20 reservation fee.
To find the maximum number of people that would make the regular admission rate a better deal, we need to compare the total cost for each option.
For the regular admission rate:
Total cost = $12.99 * n
For the group rate:
Total cost = ($8.99 * n) + $20
To determine when the regular admission rate is a better deal, the total cost for the group rate should be greater than the total cost for the regular admission rate.
($8.99 * n) + $20 > $12.99 * n
$8.99n + $20 > $12.99n
$20 > $12.99n - $8.99n
$20 > $4n
$5 > n
So, the maximum number of people that could attend your party in order for the regular admission rate to be a better deal is 5 people or less.