<PRE><B>Question 763172</B>
x is the increase to the number of scooters.  10x is the price increase.  The original formula is 500*30=15000.  The formula for the increase is:&lt;P&gt;
(500-10x) * (30+x) = 15900&lt;P&gt;
Multiply with FOIL, and simplify to get:&lt;P&gt;
{{{15000 +200x - 10x^2 = 15900}}}&lt;P&gt;
Move everything to the right side&lt;P&gt;
{{{0 = 10x^2 - 200x + 900}}}&lt;P&gt;
Divide all terms by 10:  &lt;P&gt;
{{{0 = x^2 -20x +90}}}&lt;P&gt;
Use the quadratic formula to find x:&lt;P&gt;
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} = {{{(20 +- sqrt( 400-360))/(2) }}} =&lt;P&gt;
{{{(20 +- sqrt(40))/(2) = (20 +- 2sqrt(10))/(2)= (10+-sqrt(10))}}}=&lt;P&gt;
approximately 13.16 or 6.84.&lt;P&gt;
Charge either $43.16 or $36.84&lt;P&gt;
If it has to be whole dollar increments, then charge $43 or $37.  In both cases he would make $15,910.


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