SOLUTION: the members of a flying club plan to share 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

Question 405789: the members of a flying club plan to share 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 memebers are currently in the club?
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=# of people in the club (before 5 more join)

Before they get 5 people, we have the equation:

Cost Per Individual: (since the cost is divided among "x" people)

When 5 more people join, the equation becomes

(simply replace "x" with "x+5" and subtract 2000 from "c" to form the new equation)

So we have the two equations

Equation 1

Equation 2

Start with Equation 2

Plug in (which is Equation 1)

Multiply EVERY term by the LCD to clear out the fractions.

Multiply and simplify.

Distribute

Subtract 200000x from both sides.

Combine like terms.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, a negative number of people doesn't make any sense. So we must ignore the solution

============================================================

Answer:

So the solution is which means that there are 20 members currently in the club (before the 5 people join).

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the members of a flying club plan to share 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 memebers are currently in the club?
----------------
Original average cost for x members: 200,000/x
---
New average cost for x+5 member: 200,000/(x+5)
----
Equations:
old ave - new ave = 2000
---
200,000/x - 200,000/(x+5) = 2000
---
Divide thru by 2000 to get:
100/x - 100/(x+5) = 1
----
Multiply thru by x(x+5) to get:
100(x+5) - 100x = x(x+5)
500 = x^2+5x
---
Solve: x^2+5x-500 = 0
Factor: (x-20)(x+25) = 0
Positive solution:
x = 20 (original # of members)
======
Cheers,
Stan H.
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