Question 619580
Let {{{ p }}} = the price of a lemon in cents
The number of lemons he bought was {{{ 400/p }}}
{{{ p - 4 }}} is 4 cents less than the price of a lemon
{{{ ( p - 4 )*( 400/p + 50 ) = 400 }}}
{{{ 400 + 50p - 1600/p - 200 = 400 }}}
{{{ 50p - 1600/p - 200 = 0 }}}
Multiply both sides by {{{ p }}}
{{{ 50p^2 - 1600 - 200p = 0 }}}
{{{ p^2 - 4p - 32 = 0 }}}
{{{ ( p - 8 )*( p + 4 ) = 0 }}}
{{{ p = 8 }}} 
Each lemon cost 8 cents
check:
{{{ ( p - 4 )*( 400/p + 50 ) = 400 }}}
{{{ ( 8 - 4 )*( 400/8 + 50 ) = 400 }}}
{{{ 4*( 50 + 50 ) = 400 }}}
{{{ 4*100 = 400 }}}
{{{ 400 = 400 }}} 
OK