SOLUTION: A motel charges 80.00 per day for double occupancy and 70 pr day for single occupancy. If 80 rooms are occupied one night for a total of 5800.00 how many rooms of each type are occ

Algebra ->  Systems-of-equations -> SOLUTION: A motel charges 80.00 per day for double occupancy and 70 pr day for single occupancy. If 80 rooms are occupied one night for a total of 5800.00 how many rooms of each type are occ      Log On


   

Question 232857: A motel charges 80.00 per day for double occupancy and 70 pr day for single occupancy. If 80 rooms are occupied one night for a total of 5800.00 how many rooms of each type are occupied?
Answer by eggsarecool(46) About Me  (Show Source):
You can put this solution on YOUR website!
A motel charges 80.00 per day for double occupancy and 70 pr day for single occupancy. If 80 rooms are occupied one night for a total of 5800.00 how many rooms of each type are occupied?
Ok I am goint to define x as the number of single occupancy rooms. And what this tells us is that 80-x is the number of double occupancy rooms.
So now we set up the equation.
70%2Ax%2B%2880-x%29%2A80=5800 So it is the number of single occupancy rooms times the single rate + the number of double occupancy rooms times the double rate = to the total amount made by the hotel.
Solving the equation.
70x%2B80%2A80-80x=5800
-10x%2B6400=5800 Subtract 6400 from both sides.
-10x=-600 And divide both sides by -10.
x=60 this tells us that there were 60 single occupancy rooms since I defined x as single occupancy. And double occupancy was 80-x, so 80-60=20 So there must be 20 double occupancy rooms.