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
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
But 180/8 does not equal 10????
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
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
To solve inverse variation problems, you need to set up an equation that represents the relationship between the two variables. In this case, the cost per person (C) is inversely proportional to the number of people who share (P). So, as P increases, C decreases and vice versa.
The general equation for inverse variation is C = k/P, where k is the constant of variation.
Given that the cost is $36 per person when 5 people share, we can plug in these values into the equation:
36 = k/5
To solve for k, we multiply both sides by 5:
36 * 5 = k
180 = k
Now that we have the value of k, we can use it to find the cost per person when 8 people share:
C = 180/8
Calculating this, you get C = $22.50 per person. It seems like you made the correct calculation, so let's see if the given answer of $10 per person makes sense.
Sometimes, when working with word problems, there can be additional conditions or constraints that affect the outcome. In this case, it's possible that there is some other factor in play that results in the drastic decrease in cost per person. It could be a discount for larger groups, a different pricing structure, or some restriction on booking.
Without further information, it's difficult to explain the $10 per person answer. However, based on the given equation and calculations, the correct answer appears to be $22.50 per person when 8 people share.