A hotel makes $3660 one night renting 15 double occupany rooms and 25 single occupany rooms. The double occupany rooms are $20 more than a single room. How much does each room cost?

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How do we get those equations?Well, let's set 'x' to represent the cost of a double occupancy room and 'y' to represent the cost of a single occupancy room. The hotel rented 15 doubles and 25 singles for a total of 40 rooms. Therefore, we can write our first equation:15x + 25y = 3660Since x and y are our costs for each type of room, if we were to multiply each cost by the number of rooms rented, then we should end up with our total, $3600.Now we have to find our 2nd equation. Well, a double room costs $20 more than a single. Here's our next equation:x = y + 20Now we have our system of equations:15x + 25y = 3660x = y + 20We can easily substitute (y + 20) for x since we already know what x equals! Once we plug in the values, it's just a matter of mathematics to find y, then to find x by plugging in y.After all the math, x is equal to $104 and y is equal to $84. You can always check your answer by plugging in x and y to see if the equation is true.~ Azaler