SOLUTION: A group of friends decides to buy a vacation home for $120,000, sharing the cost equally. If they could find one more person to join them, each person's contribution would drop by

Question 31262This question is from textbook College Algebra
: A group of friends decides to buy a vacation home for $120,000, sharing the cost equally. If they could find one more person to join them, each person's contribution would drop by $6,000. How many people are in the group?
Thank you so very much! This question is from textbook College Algebra

Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
Assume that the group has x number of people
Cost per head is 120,000/x
Increasing the persons by one more will make the number of persons as (x+1)
Cost per head will then be 120000/(x+1)
As per the question, 120000/(x+1) = 120000/x - 6000
=>(120000/x)-[120000/(x+1)]=6000
=>120000[1/x - 1/(x+1)]=6000
=>20[1/x - 1/(x+1)] = 1
=>20[(x+1-x)/x(x+1)]=1
=>20[1/x(x+1)]=1
=>x(x+1)=20
=>x^2+x-20=0
=>(x+5)(x-4)=0
=>x=-5 or x=4
Number of persons cannot be negative. So, total number of people in the group is 4.

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