Question 460607
Let {{{d}}} = number of days he worked
Let {{{a}}} = amount he earned per day
given:
(1) {{{ 300 = d*a }}}
(2) {{{ 300 = ( d+5 )*( a - 3 ) }}}
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(2) {{{ 300 = d*a + 5a - 3d - 15 }}}
(2) {{{ 300 = 300 + 5a - 3d - 15 }}}
(2) {{{ 5a - 3d = 15 }}}
and, from (1),
(1) {{{ a = 300/d }}}
so,
(2) {{{ 1500/d - 3d = 15 }}}
(2) {{{ 1500 - 3d^2 = 15d }}}
(2) {{{ 3d^2 + 15d - 1500 = 0 }}}
(2) {{{ d^2 + 5d - 500 = 0 }}}
{{{ d = (-b +- sqrt( b^2 - 4*a*c ))/(2*a) }}} 
{{{ a = 1 }}}
{{{ b = 5 }}}
{{{ c = -500 }}}
{{{d = (-5 +- sqrt( 5^2-4*1*(-500) ))/(2*1) }}}
{{{d = (-5 +- sqrt( 25 +  2000 )) / 2 }}}
{{{ d = ( -5 + sqrt(2025)) / 2 }}}
{{{ d = ( -5 + 45 ) / 2 }}}
{{{ d = 20 }}} ( note: can't use the (-) sqrt )
He worked 20 days
check:
(1) {{{ 300 = d*a }}}
(1) {{{ 300 = 20a }}}
(1) {{{ a = 15 }}}
(2) {{{ 300 = ( 20+5 )*( 15 - 3 ) }}}
(2) {{{ 300 = 25*12 }}}
(2) {{{ 300 = 300 }}}
OK