SOLUTION: A motel rents double rooms at $34 per day and single rooms at $25 per day. If 30 rooms were rented one day for a total of $921, how many rooms of each kind were rented?

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Question 1082516: A motel rents double rooms at $34 per day and single rooms at $25 per day. If 30 rooms were rented one day for a total of $921, how many rooms of each kind were rented?
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
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Math. model N1 (System of two equations) 

  d +   s =  30           (1)   (where d is the number of double rooms, and 
34d + 25s = 921           (2)          s is the number of double rooms)

To solve it, express s = 30-d from eq(1) and substitute it into eq(2), replacing/excluding s. 
You will get a single equation for d

34d + 25*(30-d) = 921.    (3)

From this point, you can simplify and complete the solution on your own.


This method of solution is called "substitution method".

Math. model N2 (Single equation) 

Let d = the number of double rooms.
Then the number of single rooms is (30-d),  and your "value" equation is 

34d + 25*(30-d) = 921,    (4)

which is exactly the same as eq(3).

The rest is just arithmetic.


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