Luke wants to purchase custom-made mugs to advertise his business. Two companies offer different deals: Company A: Pay a design fee of $30.00, plus $4.50 per mug or Company B: Pay a design fee of $40.00, plus $4.25 per mug

(a) State a linear function f (x) that represents Company A's total charge for an order of x mugs.

(b) State a linear function g(x) that represents Company B's total charge for an order of x mugs.

(c) Luke wants to purchase 50 custom-made mugs, as cheaply as possible. With which company should he place his order? Show work/explanation.

(d) For what number of mugs is the total charge exactly the same for both companies? Show algebraic work/explanation.

(e) Fill in the blanks: Company B is the cheaper option if more than ______ (enter number) mugs are ordered. Careful!!