Question

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

Answer 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

Answer 2

But 180/8 does not equal 10????

Answer 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

Answer 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