Question 1086340
I think this problem is assuming Lee
spends the same amount each day
Let {{{ d }}} = the number of days he actually stays
{{{ 1200/d }}} = the amount he actully spent each day
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{{{ 1200 = ( 1200/d - 50 )*( d + 2 ) }}}
{{{ 1200 = 1200 - 50d + 2400/d - 100 }}}
{{{ 2400/d = 50d + 100 }}}
{{{ 2400 = 50d^2 + 100d }}}
{{{ 48 = d^2 + 2d }}}
complete the square
{{{ d^2 + 2d + 1 = 48 + 1 }}}
{{{ ( d + 1 )^2 = 49 }}}
{{{ d + 1 = 7 }}}
{{{ d = 6 }}}
{{{ d = 6 }}}
His holiday was 6 days
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check:
{{{ 1200 = ( 1200/d - 50 )*( d + 2 ) }}}
{{{ 1200 = ( 1200/6 - 50 )*( 6 + 2 ) }}} 
{{{ 1200 = ( 200 - 50 )*8 }}}
{{{ 1200 = 150*8 }}}
{{{ 1200 = 1200 }}}
OK