Question 191945

Let {{{x}}}= the number of melons bought originally
Given:
{{{200/x}}}= Original cost per melon
{{{200/x + 1.5}}}= Selling price per melon
{{{x - 30}}}= number of melons sold
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{{{200 = (200/x + 1.5)*(x - 30)}}}
{{{200 = 200 - 6000/x - 45 + 1.5x}}}
{{{6000/x - 1.5x + 45 = 0}}}
{{{6000 - 1.5x^2 + 45x = 0}}}
{{{-1.5x^2 + 45x + 6000 = 0}}}
{{{-15x^2 + 450x + 60000 = 0}}}
{{{-x^2 + 30x + 4000 = 0}}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = -1}}}
{{{b = 30}}}
{{{c = 4000}}}
{{{x = ( 30 +- sqrt(  30^2 - 4*(-1)*4000 ))/(2*1) }}} 
{{{x = (30 +- sqrt( 900 + 16000 ))/ 2 }}}
{{{x = (30 +- sqrt( 16900 ))/ 2 }}}
{{{x = (30 +- 130)/2}}}
{{{x = 160/2}}}
{{{x = 80}}}
She bought 80 melons originally
check answer:
{{{200 = (200/x + 1.5)*(x - 30)}}}
{{{200 = (200/80 + 1.5)*(80 - 30)}}}
{{{200 = (2.5 + 1.5)*(50)}}}
{{{200 = 4*50}}}
{{{200 = 200}}}
OK