Question 282341
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A group plans to share the cost equally for a $200,000 plane, the group wants to find 5 more people to join,
so that the cost will decrease $2,000 per person. How {{{highlight(many)}}} people are currently in the group ?
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        The solution by @mananth is incorrect due to arithmetic errors inside of it.

        I came to bring a correct solution.



<pre>
The original scenario is  {{{200000/x}}}  dollars per person.

The other scenario is  {{{200000/(x+5)}}}  dollars per person.


The setup equation is

    {{{200000/x}}} - {{{200000/(x+5))}}} = 2000.


Divide both side by 1000 to make writing easier

    {{{200/x}}} - {{{200/(x+5))}}} = 2.


Reduce it to the quadratic equation

    x^2 + 5x - 5000 = 0.


Factor left side

    (x+25)*(x-20) = 0.


The roots are  x= -25  and  x= 20.


Since we look for a price, we accept the positive root and reject the negative one.


<U>ANSWER</U>.  Currently/originally the group is 20 people.
</pre>

Solved correctly.