$20.$ Ned$$s Sheds purchases building materials from Timbertown Lumber for $$3,700$ with terms of

$4/15,$ n$/30.$ The invoice is dated October $17.$ Ned$$s decides to send in a $$2,000$ partial payment.

a$.$ By what date must the partial payment be sent to take advantage of the cash discount?

b$.$ What is the net date?

c$.$ If partial payment was sent by the discount date, what is the balance still due on the order?