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?
both graphs have the same price at 5 people
A. 2 people
B. 3 people
C. 4 people
D. 5 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 per person for each option.
For the regular admission, the cost per person is $12.99.
For the group rate, the cost per person is $8.99, plus the $20 reservation fee. So the total cost per person for the group rate is $8.99 + $20 = $28.99 / total number of people.
We need to find the point at which the total cost per person for the group rate is greater than the cost per person for the regular admission.
So, we set up the equation:
$12.99 * n = $28.99 / n
Where n is the total number of people.
To solve for n, we can multiply both sides of the equation by n:
$12.99 * n^2 = $28.99
Divide both sides by $12.99:
n^2 = $28.99 / $12.99
n^2 = 2.23
Take the square root of both sides to isolate n:
n = sqrt(2.23)
n ≈ 1.49
Since we can't have a fraction of a person, we round down to the nearest whole number.
Thus, the maximum number of people that could attend the party for the individual admission rate to be a better deal is 1 person.