SOLUTION: A motel rents double rooms at $35 per day and single rooms at $23 per day. If 27 rooms were rented one day for a total of $849, how many rooms of each kind were rented?

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: A motel rents double rooms at $35 per day and single rooms at $23 per day. If 27 rooms were rented one day for a total of $849, how many rooms of each kind were rented?      Log On

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Question 473426: A motel rents double rooms at $35 per day and single rooms at $23 per day. If 27 rooms were rented one day for a total of $849, how many rooms of each kind were rented?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x + y = 27 (first equation)
23*x + 35*y = 849 (second equation)
x equals the number of single rooms
y equals the number of double rooms
use first equation to solve for y in terms of x.
you get y = 27-x
substitute for y in the second equation to get:
23*x + 35*(27-x) = 849
this equation becomes:
23*x + 35*27 - 35*x = 849
combine like terms to get:
-12*x + 945 = 849
subtract 945 from both sides of the equation to get:
-12*x = 849-945 = -96
divide both sides by -12 to get:
x = -96/-12 = 8
since x+y = 27, this means that:
x = 8
y = 19
8*23 + 19*35 = 184 + 665 = 849
everything checks out.
x+y = 27
23*x + 35*y = 849
answer is:
x = 8 = number of single rooms.
y = 19 = number of double rooms.