Question 995048
Finding the actual counts of each persons' candies seems most direct.


c:s is  4:6;
{{{system(c/s=4/6,s=c+6)}}}
{{{c=(2/3)s}}}
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{{{s=(2/3)s+6}}}
{{{s-2s/3=6}}}
{{{3s-2s=18}}}
{{{highlight(s=18)}}}


{{{c=(2/3)s=(2/3)18=12}}}
{{{highlight(c=12)}}}


Sara gives {{{18/2=9}}} of her pieces to Charlie.
Sarah:  {{{18-9=9}}}
Charlie:  {{{12+9=21}}}
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Now, the new ratio c:s  is  21:9  or <b>7:3</b>.