math

Inverse Variation
I'm doing something wrong in my calculation but I can't figure out what --

The cost per person to rent a mountain cabin is inversely proportional to the number of people who share the rent. If the cost is $36 per person when 5 people share, what is the cost per person when 8 people share?

So I did?
C = cost per person
k = the constant
P = number of people

36 = k/8
k = 180

c = 180/8 = $22.50 per person

However, the answer says it is $10 per person

Honestly, I can't see how the price can go down so drastically, from $36 per person for 5 people to $10 per person for 8 people-- but I must be making an error

Thank you

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  1. you are not matching the corresponding information
    When you have 5 people, the cost is 36, you matched 8 with 36
    so
    36 = k/5 and k = 180

    then cost = 180/p
    so when p = 8
    cost = 180/8 = 10

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    Reiny
  2. But 180/8 does not equal 10????

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  3. Of course not, don't know what I was thinking ....
    I saw your 36 = k/8 and assumed that is where the error was.

    New start
    cost = k/p
    when cost = 36, p = 5
    36 = k/5 ----> k = 180

    so Cost = 180/p
    when p = 8
    cost = 180/8 = 22.50

    If the wording is as you typed it, the 22.50 is the correct answer, it can't be $10

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    Reiny
  4. The cost per person (c) .. is inversely proportional to the number of people (n)
    So,
    cn = k, a constant.
    So, you want c such that
    c*8 = 5*36

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    oobleck

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