A typical home in the northern U$.$S$.$ might require $120$MBtu of heat for the average winter.

a$.$ If this heat were supplied by a natural gas furnace operating at $60$ percent efficiency, how many cubic feet of gas would need to be purchased?

b$.$ At a cost of $$\frac{0\mathrm{.}90}{c}cf,$ what would it cost to heat this house for one sons

c$.$ If a new $80$ percent efficient furnace could be installed at a cost of $$4,000,$ how long would it take to pay back the cost of this furnace assuming gas prices remained the same?