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

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) (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:

.
Multiply through by to eliminate the denominators.
.

.
Divide by 2000

.
The 100x cancel, so collect terms and rearrange

.
Multiply by -1

.
Factor

.
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

.
average cost with 25 members

.
So the difference in average cost is 2000, as the problem requires.
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