Question 701769
Let {{{ k }}} = the number of kilos of mangoes she bought
She sold {{{ k - 3 }}} kilos 
{{{ 8*( k - 3 ) }}} = her total profit
{{{ 200 + 8*( k - 3 ) }}} = the amount she received
{{{ 200 + 8k - 24 = 176 + 8k }}}
She can now buy {{{ k + 2 }}} kilos at {{{ 200/k }}} pesos / kilo
{{{ 176 + 8k = ( k + 2 )*( 200/k ) }}}
{{{ 176 + 8k = 200 + 400/k }}}
{{{ 8k = 24 + 400/k }}}
{{{ 8k^2 = 24k + 400 }}}
{{{ 8k^2 - 24k - 400 = 0 }}}
{{{ k^2 - 3k - 50 = 0 }}}
Use quadratic equation
{{{ k = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = 1 }}}
{{{ b = -3 }}}
{{{ c = -50 }}}
{{{ k = (-(-3) +- sqrt( (-3)^2 - 4*1*(-50) )) / (2*1) }}} 
{{{ k = ( 3 +- sqrt(  9 + 200 )) / 2 }}} 
{{{ k = ( 3 +- 14.4568 ) / 2 }}} 
{{{ k = 17.4568 / 2 }}}
{{{ k = 8.728 }}}
She bought 8.728 kilos
at a cost of {{{ 200 / 8.728 = 22.915 }}} pesos
Hope I got it