SOLUTION: I need help finding the formula to solve this word problem. The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more p

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Question 201205: I need help finding the formula to solve this word problem. 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?
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) 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



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Answer:


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

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




is the amount it will cost each person before they find the five new members.



is the amount that each person will pay if they add 5 members.

These two amounts differ by $2,000, so:



Just solve for . Hint: I would start by multiplying both sides of this equation by . You will end up solving a quadratic. Remember to exclude the negative root. Having a negative number of members doesn't make sense.


John