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 p

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Question 246003: 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?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The club has x members now, so the average cost = 200,000/x.
If they add 5 members, the average cost = 200,000/(x+5) - 2000.
So, we can express this as:
%0D%0A200000%2Fx+=+200000%2F%28x%2B5%29+%2B+2000%0D%0A
.
%0D%0A200000%2Fx+-+200000%2F%28x%2B5%29+-+2000+=+0%0D%0A
.
Multiply through by x%28x%2B5%29 to eliminate the denominators.
.
%0D%0A200000%28x%2B5%29+-+200000x+-+2000%28x%29%28x%2B5%29+=+0%0D%0A
.
%0D%0A200000%28x%2B5%29+-+200000x+-+2000x%5E2+-+10000x+=+0%0D%0A
.
%0D%0A200000x+%2B+1000000+-+200000x+-+2000x%5E2+-+10000x+=+0%0D%0A
.
Divide by 2000
%0D%0A100x+%2B+500+-+100x+-+x%5E2+-+5x+=+0%0D%0A
.
The 100x cancel, so collect terms and rearrange
%0D%0A-x%5E2+-+5x+%2B+500+=+0%0D%0A
.
Multiply by -1
%0D%0Ax%5E2+%2B+5x+-+500+=+0%0D%0A
.
Factor
%0D%0A-%28x%2B25%29%28x-20%29+=+0%0D%0A
.
So x can = either -25 or 20. -25 members does not make sense, so x = 20 and x+5 = 25.
.
Checking our answer.
average cost with 20 members
200000%2F20+=+10000%0D%0A
.
average cost with 25 members
200000%2F25+=+8000%0D%0A
.
So the difference in average cost is 2000, as the problem requires.