Question 648743
Let {{{ c }}} = number of cookies he started with
After giving some to Mom, he has left
{{{ c - c/2 - 1/2  = c/2 - 1/2 }}} 
After giving some to Aunt, he has left
{{{ c/2 - 1/2 - ( c/4 - 1/4 ) - 1/2 = c/4 - 3/4 }}}
After giving some to a friend he has left
{{{ c/4 - 3/4 - (1/2)*( c/4 - 3/4 ) - 1/2  = c/8 - 7/8 }}}
He ends up with 6 cookies, so
{{{ c/8 - 7/8 = 6 }}}
{{{ c - 7 = 48 }}}
{{{ c = 55 }}}
He started with 55 cookies
check answer:
He gave Mom {{{ 55/2 + 1/2 = 56/2 }}}
{{{ 56/2 = 28 }}}, 
so he has left {{{ 55 - 28 = 27 }}} 
He gave Aunt {{{ 27/2 + 1/2 = 28/2 }}}
{{{ 28/2 = 14 }}},
so, he has left {{{ 27 - 14 = 13 }}}
He gave friend {{{ 13/2 + 1/2 = 14/2 }}}
{{{ 14/2 = 7 }}}
He has left {{{ 13 - 7 = 6 }}}
OK