Jill’s business hosting birthday parties for children has been very successful. She now offers a special party package for large parties.

1. For her large party package, the party is held in a private room at a pizza parlor. The pizza parlor charges $\$300$ for the use of the room, plus $\$7.00$ per guest. Write a function that represents the cost per guest for a party.

   Hint (a):

   Use $x$ as the number of guests.
   Which cost is dependent on $x$?

   Answer (a):

   $f(x) = 300 + 7x$

2. If Jill charges $\$50$ per guest for the party package, write a function to represent her profit.

   Hint (b):

   Profit is the total amount you make minus the amount it costs to hold the party.

3. Jill wants to make at least $\$100$ profit each time she hosts a party. Write an inequality to represent this situation. What should she require as the minimum number of guests for the large party package?

   Hint (c):

   Use your equation from part (b) and the fact that this amount must be more than $100$.