show work please

6.11 Motley Motel's potential average room rate is calculated to be $31.00. Assume that this motel had three market segments. Vacation travellers comprise 75% of the room nights and are charged 100% of the rack rate. Business travellers comprise 15% of the room nights and are charged 90% of the rack rate. Sports teams account for 10% of the room nights and are charged 80% of the rack rate. a. Calculate the room rate by market segment. b. Prove that your calculations are correct, assuming that total annual room nights are 7,300