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For a convention, a hotel charges a daily room rate of $120 [#permalink]

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17 Oct 2008, 09:31

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For a convention, a hotel charges a daily room rate of $120 for 1 person and x dollars for each additional person. What is the charge for each additional person?

(1) The daily cost per person for 4 people sharing the cost of a room equally is $45. (2) The daily cost per person for 2 people sharing the cost of a room equally is $25 more than the corresponding cost for 4 people.

For a convention, a hotel charges a daily room rate of $120 for 1 person and x dollars for each additional person. What is the charge for each additional person? (1) The daily cost per person for 4 people sharing the cost of a room equally is $45. (2) The daily cost per person for 2 people sharing the cost of a room equally is $25 more than the corresponding cost for 4 people.

Slightly longer explanation:

Statement 1: If the average is $45, then the total cost per day is 4(45) = 180 With 4 people the cost is $120 + x + x + x So, we get the equation 120 + 3x = 180 (clearly, we COULD solve this equation for x) --> sufficient

Statement 2: The average cost for 2 people is (120+x)/2 The average cost for 4 people is (120+3x)/4 We know that the first average cost is $25 more than the second average, so we can create the equation (120+x)/2 = (120+3x)/4 + 25 (clearly, we COULD solve this equation for x) --> sufficient

IMO D. A. If for each person the daly rate is 45$ than 45*4=280. 280-120=160 This is the additional payment that the 3 additional people in the room would have to pay. 160/3 is the rate that each of this 3 people would have to pay. Sufficient. B. The room rate for 2 people = (120+X). The room rate for 4 people= (120+3*Y). In addition we know that X = 25+Y. So we have 2 integers and two equations. Sufficient.

Not clear with the second statement. Can anybody clear this please.

(i) daily cost per person in the case of two persons: (120+x)/2; (ii) daily cost per person in the case of four persons: (120+3x)/4. Keeping in view the difference of $25, we make an equation: (120+x)/2 - 25 = (120+3x)/4 240+2x-100 = 120+3x 240-100-120=3x-2x X=20

Re: For a convention, a hotel charges a daily room rate of $120 [#permalink]

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25 Jun 2015, 04:02

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Re: For a convention, a hotel charges a daily room rate of $120 [#permalink]

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09 Jul 2016, 06:56

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