The manager of an e$-$learning company identified a new course that they could create and sell for $$100$ per student. The costs for adding this new course to their product offering would be: $$2,100$ per month to lease additional space, $$290$ per month for insurance, $$4,900$ per month for support staff, $$3,600$ per month for sales staff, and variable costs of $$4$ per student. They can sell to a maximum of $750$ students per month.

a$.$ For the company to break tiven per month, how many students would have to purchase the course?

Round up to the next whole number

b$.$ If they made a profit of $$34,650$ last month, how many students purchased the course?