A motel in Florida charges $90 per day for double occupancy and $80 for single occupancy. If 80 rooms are occupied for a total of $6930, how many rooms of each kind are occupied?

x = number of $90 per day rooms

80 - x = number of $80 per day rooms {there are 80 total occupied rooms}

90x + 80(80 - x) = 6930 {value of room times number of rooms equals total value}

90x + 6400 - 80x = 6930 {used distributive property}

10x + 6400 = 6930 {combined like terms}

10x = 530 {subtracted 6400 from each side}

x = 53 $90 per day rooms {divided each side by 10}

80 - x = 27 $80 per day rooms {substituted 53, in for x, into 80 - x}

**53 $90 per day rooms**

and

27 $80 per day rooms

and

27 $80 per day rooms

*- Algebra House*