SOLUTION: Sharing cost. The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per pe

Question 281982: Sharing cost. The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by $2000. How many members are currently in the club?
Found 2 solutions by josmiceli, ptaylor:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = current number of members in club
Let = current cost per person
given:

-------------------------
By substitution:

Multiply both sides by

divide both sides by

(the negative root is invalid)
There are currently 20 members
check:

and

OK
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=number of members currently in the club
($ understood)
cost per person=(200,000)/x
With five more people in the club the cost per person would be (200,000)/(x+5)
Now we are told that:
{(200,000)/x}-2000=(200,000)/(x+5) multiply each term by x(x+5)
(200,000)(x+5)-2000x(x+5)=200,000x get rid of parens
200,000x+1,000,000-2000x^2-10,000x=200,000x divide each term by 2000
100x+500-x^2-5x=100x subtract 100x from each side and then multiply each term by -1
x^2+5x-500=0---quadratic in standard form and it can be factored
(x+25)(x-20)=0
x=-25----------------------no good members are positive
x=20--------------------number of members currently in the club
CK
200,000/20=$10,000 per member
200,000/25=$8000 per member or $2000 less per member
Hope this helps---ptaylor
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