Question 628555
Let {{{ d }}} = the actual number of days he worked
{{{ 192/d }}} = the actual amount of money he made each day
{{{ 192/d + 8 }}} = the amount of money he made each day plus $8
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given:
( daily earnings + $8 ) = ( daily earnings ) x ( 2 less days worked )
{{{ 192/d + 8 =  192 / (d-2)  }}}  
Multiply both sides by {{{ d*( d - 2 ) }}}
{{{ 192*( d-2 ) + 8*d*( d-2 )  = 192d }}}
{{{ 192d - 384 + 8d^2 - 16d = 192d }}}
{{{ 8d^2 - 16d = 384 }}}
{{{ d^2 - 2d = 48 }}}
Complete the square
{{{ d^2 - 2d + (-2/2)^2 = 48 + (-2/2)^2 }}}
{{{ d^2 - 2d + 1 = 49 }}}
{{{ ( d - 1 )^2 = 7^2 }}}
{{{ d - 1 = 7 }}}
{{{ d = 8 }}}
He worked 8 days
check:
{{{ 192/d + 8 =  192 / (d-2)  }}}  
{{{ 192/8 + 8 =  192 / (8-2)  }}}  
{{{ 24 + 8 = 192/6 }}}
{{{ 32 = 32 }}}
OK