Question 143218: A family on vacation booked three different types of rooms at a hotel, a standard, double and a suite at an average price of US$140 per room. if they were to book only the standard and the suite the average price would reduce to US$135. How much does the suite cost?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! You won't be able to derive a specific answer, because you have three variables and only two defined relatiionships.
Cost of standard: x
Cost of double: y
Cost of suite: z
Average of the 3 is 140, so 
Average of standard and suite is 135, so 
So you can say that  and  .
So 
Substituting:
 which is to say  , so we know the price of a double, but as for the standard and suite, all you know is that they add up to 270. The standard could be $1 and the suite $269, or the standard could be $90 and the suite $180 -- or any other combination that totals 270. So all you can say for sure about the cost of the suite is that it is $270 minus the cost of the standard -- whatever it is.
From a practical point of view, you would expect the suite to be greater than $150. After all, who would then book a double room if you could get the suite for the same money? By the same logic, the standard room must be less than $120 otherwise the suite could not be greater than $150.
So, for the suite, the cost must be an element of the set of all z such that z * 100 is an integer (can't make change smaller than a penny), 150 < z << 270. (<< means 'a lot less than'). z has to be 'a lot less than' 270, otherwise the hotel would be charging too little for the standard rooms.
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