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?

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*x+(80-x)*80=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+80*80-80x=5800}}}
{{{-10x+6400=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.