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

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> 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       Log On

Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

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(28595) About Me  (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: c=200000%2Fx (since the cost is divided among "x" people)


When 5 more people join, the equation becomes


c-2000=200000%2F%28x%2B5%29 (simply replace "x" with "x+5" and subtract 2000 from "c" to form the new equation)


So we have the two equations


c=200000%2Fx Equation 1


c-2000=200000%2F%28x%2B5%29 Equation 2



c-2000=200000%2F%28x%2B5%29 Start with Equation 2


200000%2Fx-2000=200000%2F%28x%2B5%29 Plug in c=150000%2Fx (which is Equation 1)


Multiply EVERY term by the LCD x%28x%2B5%29 to clear out the fractions.


200000%28x%2B5%29-2000x%28x%2B5%29=200000x Multiply and simplify.


200000x%2B1000000-2000x%5E2-10000x=200000x Distribute


200000x%2B1000000-2000x%5E2-10000x-200000x=0 Subtract 200000x from both sides.


-2000x%5E2-10000x%2B1000000=0 Combine like terms.


Notice that the quadratic -2000x%5E2-10000x%2B1000000 is in the form of Ax%5E2%2BBx%2BC where A=-2000, B=-10000, and C=1000000


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


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


Plug in A=-2000, B=-10000, and C=1000000


Negate -10000 to get 10000.


x+=+%2810000+%2B-+sqrt%28+100000000-4%28-2000%29%281000000%29+%29%29%2F%282%28-2000%29%29 Square -10000 to get 100000000.


x+=+%2810000+%2B-+sqrt%28+100000000--8000000000+%29%29%2F%282%28-2000%29%29 Multiply 4%28-2000%29%281000000%29 to get -8000000000


x+=+%2810000+%2B-+sqrt%28+100000000%2B8000000000+%29%29%2F%282%28-2000%29%29 Rewrite sqrt%28100000000--8000000000%29 as sqrt%28100000000%2B8000000000%29


x+=+%2810000+%2B-+sqrt%28+8100000000+%29%29%2F%282%28-2000%29%29 Add 100000000 to 8000000000 to get 8100000000


x+=+%2810000+%2B-+sqrt%28+8100000000+%29%29%2F%28-4000%29 Multiply 2 and -2000 to get -4000.


x+=+%2810000+%2B-+90000%29%2F%28-4000%29 Take the square root of 8100000000 to get 90000.


x+=+%2810000+%2B+90000%29%2F%28-4000%29 or x+=+%2810000+-+90000%29%2F%28-4000%29 Break up the expression.


x+=+%28100000%29%2F%28-4000%29 or x+=++%28-80000%29%2F%28-4000%29 Combine like terms.


x+=+-25 or x+=+20 Simplify.


So the possible answers are x+=+-25 or x+=+20


However, a negative number of people doesn't make any sense. So we must ignore the solution x=-25



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

Answer:


So the solution is x+=+20 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(57377) About Me  (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.