PSAT/SAT & ACT Math Attack – Ice Rink Party

To rent a room for a party at an ice-skating rink, the charge is $50 per hour plus $2 per person attending the party. Which of the following functions represents the charge, in dollars, to rent a room at the rink for a 2-hour party if n people attend the party?

A. f(n) = 102n

B. f(n) = 200n

C. f(n) = 100n + 2

D. f(n) = 100 + 2n

E. f(n) = 100 + 2n

Explanation: If the charge to rent a room is $50/hour, and you are trying to rent a room for 2 hours, you know the cost of just renting the room is:

$50/hour x 2 hours = $100

Any additional cost for renting the room is associated with the number of people who attend the party. The charge is $2 per person, or:

$2n

Added together, these two values are the total amount to rent a room at the ice-skating rink for a party. The total amount of money it would cost, represented as an equation, looks like:

$100 + $2n

Because we are being asked to express this as a function in dollars, we must express it as such:

f(n) = 100 + 2n

The answer is therefore (D).

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