Florida hotel rooms money problem

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?

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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

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