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

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) (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).
Answer by solver91311(24713) (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

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