SOLUTION: please someone help me with this word problem please I tried to do it myself but keep getting it wrong.. The members of the flying club plan to share equally the cost of a $2

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Question 185194: please someone help me with this word problem please I tried to do it myself but keep getting it wrong..

The members of the 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?
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the current cost per person and let x be the current number of members. Also, for convenience sake, represent the money amounts in thousands, meaning the cost of the airplane is 200 and the savings after recruiting 5 new members is 2. Then:

thousand dollars.

If you add five new members reducing the cost per person by 2 thousand, then:

Add on the left with x as the common denominator:

And now we have a proportion:

Cross-multiply:

Expand, collect terms, put in standard form:

Divide by -2:

Factor the quadratic and eliminate the negative root because a negative number of members is absurd -- it is an extraneous root introduced by squaring the variable in the process of solving the problem. The positive root is your current number of members.

Check your answer by dividing 200 by your result for x and verify that the quotient is 2 larger than the result of dividing 200 by x + 5.

John