Question 176375: 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 $2,000. How many members are currently in the club?
Found 2 solutions by EMStelley, MathLover1:
Answer by EMStelley(208)   (Show Source):
You can put this solution on YOUR website! Call the number of people currently in the club x. Then if they share the cost equally, they will each pay $200,000/x. Now, if they find 5 more people the cost will decrease by 2,000 per person. So if x is increased by 5, (x+5), the cost, $200,000/(x+5) will be 2,000 less per person, a.k.a. $200,000/x - 2000. So we need to set those two equal to each other and solve for x.
Now, if you are anything like most people, than I would assume you don't like working with fractions. So how about we try to get rid of them? If we multiplied both sides by x would that work? No, it would not get rid of the fraction on the left hand side. If we multiplied both sides by x+5 would that work? No again, as it would not correct the fraction on the right hand side. It seems that we need both. So let's multiply by x(x+5) on both sides:
Now, subtract 200000x from both sides to obtain:
Rearranging, we have a quadratic:
Now, these are all fairly large numbers. Do they have anything in common? They all have at least a factor of 2000 in them, so let's divide both sides by -2000 to get rid of it:
So now, we need to solve this quadratic equation. I will use the quadratic formula:
Here, a=1, b=5, c=-500, so
So,
and
However, it's not possible to have -25 people in a club, so the only feasible solution here is 20.
Answer by MathLover1(20855)  (Show Source):
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