Question 181076: The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want five more people to join the club so that the cost per person will decrease by $2,000. How many members are currently in the club?
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! The original cost for members was 200,000/x
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The new cost is 200,000/(x+5) and we are told that this new cost is 2,000 more than the old cost.
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So,
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The next step is to multiply the whole equation by x(x+5) this will eliminate all fractions. Note that x*(x+5)=x^2+5x
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Notice that x in the denominator on the left cancels with the x that it has been multiplied by. Also the (x+5) on the right does the same thing to that fraction. So you have.
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for the last term on the right I multiplied 2000 by (x^2+5x)
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Now you have to foil out the term on the left. The 200,000x, which is on both sides of the equation, will cancel. Using scientific notation the equation you have will look like this when you move everything over to the left.
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divide all terms by 2000
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Not interested in the negative root here, because it is physically impossible to have negative membership in the club.
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so the answer is x=20 members currently in club
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| Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=2025 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 20, -25.
Here's your graph:
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