$200K cost shared between members; $2K less w/ 5 more member

algebraiseasy

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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?

This is the question but I don't know the equation. I know the answer but I need to know how to work it. Thanks!
 
Re: algebra

x = current members

200000/x - 200000/(x+5) = 2000 ; solve for x
 
algebraiseasy said:
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?
If two people split a cost of $12, how do you find how much each pays?

If then three people split that $12, how do you find how much each pays?

If now four people split that $12, how do you find how much each pays?

Use the same reasoning here. They started with, say, "x" people splitting $200,000. What expression represents how much each person paid?

They then got five more people. What expression stands for this new number of people? What expression stands for the new per-person amount?

You are told that (new per-person amount) is (original per-person amount) less (two thousand). Translate this into an equation, and solve for the variable.

If you get stuck, please reply showing your steps and reasoning. Thank you! :D
 
I see how you get the equation but now I'm having trouble solving it. Do we multiply both sides by (x+5) to get rid of the denominator? Leaving us:1,000,000-200,000=2000x+10,000?
 
algebraiseasy said:
I see how you get the equation but now I'm having trouble solving it. Do we multiply both sides by (x+5) to get rid of the denominator?
There are two denominators, as you saw when you derived the equation yourself. How are you handling that? How did the right-hand side, (2000)(x + 5) when you did the multiplication, "simplify" as just "2000"?

Please be complete. Thank you! :D
 
I think I should multiply both sides by the common denominator x(x+5). That would give me 200,000x +1,000,000-200,000x=2000x^2 + 10,000x
1,000,000=2000x^2 +10,000x
x^2 + 5x - 1000 = 0
This is not correct
 
algebraiseasy said:
I think I should multiply both sides by the common denominator x(x+5). That would give me 200,000x +1,000,000-200,000x=2000x^2 + 10,000x
1,000,000=2000x^2 +10,000x
x^2 + 5x - 1000 = 0
This is not correct
1,000,000 / 2000 = 500 (not 1000) : kick yourself :wink:
 
Thank you so much! You have been very helpful and I wish I could kick myself. I just started a new workout routine and I'm too sore! :D
 
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