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?
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To solve this problem, let's first assign variables to the unknown values mentioned in the problem:
Let "x" represent the current number of members in the club.
Given that the cost of the airplane is $200,000, we can set up the following equation:
Total cost / Number of members = Cost per person
$200,000 / x = Cost per person (Equation 1)
The members want the cost per person to decrease by $2,000 when five more people join. This would mean the new cost per person is equal to the current cost per person minus $2,000:
Current cost per person - $2,000 = New cost per person
Cost per person - $2,000 = New cost per person (Equation 2)
By substituting Equation 1 into Equation 2, we can set up an equation based on the current number of members:
($200,000 / x) - $2,000 = ($200,000 / (x + 5))
Now, let's solve this equation to find the current number of members:
$200,000 - $2,000x = $200,000 - $2,000(x + 5)
Simplifying the equation:
$200,000 - $2,000x = $200,000 - $2,000x - $10,000
$10,000 = $10,000
Since the equation simplifies to a true statement, we conclude that the current number of members (x) can be any value. This means we don't have enough information to determine the current number of members in the club.