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Question
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?
Responses
A 2 people2 people
B 3 people3 people
C 4 people4 people
D 5 people5 people
E 6 people
To find the maximum number of people that could attend the party for the individual admission rate to be a better deal, we need to compare the total cost for both options.
For the individual admission rate:
Cost per person = $12.99
Total cost for a group of n people = $12.99 * n
For the group rate:
Cost per person = $8.99
Reservation fee = $20
Total cost for a group of n people = ($8.99 * n) + $20
Now we can set up an inequality to find the maximum value of n:
$12.99 * n < ($8.99 * n) + $20
Subtracting ($8.99 * n) and $20 from both sides:
$12.99 * n - ($8.99 * n) - $20 < 0
Simplifying:
$4.00 * n - $20 < 0
Adding $20 to both sides:
$4.00 * n < $20
Dividing both sides by $4.00:
n < 5
Since the number of people cannot be a decimal or fraction, the maximum number of people that could attend the party for the individual admission rate to be a better deal is 4 people.
Therefore, the answer is C) 4 people.