Question 197937
Let {{{w}}}= the number of watermelons bought
given:
{{{w - 30}}}= the number of watermelons sold
{{{1.5*(w - 30)}}}= profit made on watermelons sold
{{{200/w}}}= price paid per watermelon bought
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{{{(200/w + 1.5)*(w - 30) = 200}}}
This is (cost/wm + profit/wm)*(actual wm's sold) = investment
{{{200/w + 1.5 = 200/(w - 30)}}}
Multiply both sides by {{{w*(w - 30)}}}
{{{200*(w - 30) + 1.5w*(w - 30) = 200w}}}
{{{200w - 6000 + 1.5w^2 - 45w = 200w}}}
{{{1.5w^2 - 45w - 6000 = 0}}}
{{{w = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1.5}}}
{{{b = -45}}}
{{{c = -6000}}}
{{{w = (-(-45) +- sqrt( (-45)^2-4*1.5*(-6000) ))/(2*1.5) }}}
{{{w = (45 +- sqrt( 2025 + 36000 ))/3 }}}
{{{w = (45 +- sqrt( 38025 ))/3 }}}
{{{w = (45 +- 195)/3 }}}
{{{w = 240/3}}} (ignore negative result)
{{{w = 80}}}
She bought 80 watermelons originally
check answer:
{{{200/80 = 2.5}}}= price paid per watermelon
{{{80 - 30 = 50}}}= watermelons sold
{{{2.5*50 = 125}}}= price paid for water melons sold
{{{1.5*50 = 75}}}= profit on watermelons sold
{{{125 + 75 = 200}}}
OK