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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 determine when the individual admission rate is a better deal, we need to compare the cost per person under the regular rate to the cost per person under the group rate.
For the regular rate, the cost per person is $12.99.
For the group rate, the cost per person is $8.99 + $20 reservation fee, which is a total of $28.99 divided by the number of people attending the party.
Therefore, we need to find the maximum number of people for which the cost per person under the group rate is less than $12.99.
Let's set up the equation:
$12.99 > $28.99/n
where n is the number of people attending the party.
Dividing both sides of the inequality by $12.99:
1 > $28.99/$12.99n
Multiplying both sides of the inequality by $12.99n:
$12.99n > $28.99
Dividing both sides of the inequality by $12.99:
n > $28.99/$12.99
Simplifying:
n > 2.23
Since the number of people attending must be a whole number, the maximum number of people that could attend your party in order for the individual admission rate to be a better deal is 3 people (option B).