Question 132900This question is from textbook
: A group of people want to share equally the cost of a $200,000 airplane. They want to find 5 more people to join their club so that the cost per person decreases by $2000. How many people are currently in the club?
This question is from textbook
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
Let x=number of people currently in the club
Cost per person=($200,000/x)
With 5 more people in the club, the per-person cost would be 200,000/(x+5)
Now we are told that ($ are understood):
(200,000/x)-200,000/(x+5)=2000 divide each term by 2000
(100/x)-(100/(x+5))=1 multiply each term by x(x+5)
100(x+5)-100x=x(x+5) get rid of parens
100x+500-100x=x^2+5x subtract 500 from each side
100x+500-500-100x=x^2+5x-500 collect like terms
x^2+5x-500=0 quadratic in standard form and it can be factored
(x+25)(x-20)=0
x+25=0
x=-25 ---------------------Disregard people are positive in this case
and
x-20=0
x=20-----------------------------number of people currently in the club
CK
200,000/20-200,000/25=2000
10,000-8000=2000
2000=2000
Hope thsi helps---ptaylor
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