Question 739840
N = Original number of sweets in the bag.


Son:  {{{highlight(1+(1/7)N)}}} received.



Number of sweets remaining in bag is {{{R= N-(1+(1/7)N)}}}.  The variable R is assigned as the number of sweets now REMAINING in the bag after the son received his allotment of sweets.


Daughter:  {{{2+(1/7)(R)}}} which is substituting for R,
{{{2+(1/7)( N-(1+(1/7)N))=2+(1/7)(N-1-N(1/7)^2)}}}
=2+N/7-1/7-N/(7^2)
={{{highlight(2+N/7-1/7-N/(7^2))}}} received.


Each child has the same number of sweets:
{{{2+N/7-1/7-N/(7^2)=1+(1/7)N}}}
Multiply left and right members by {{{7^2}}},
{{{98+7N-7-N=49+7N}}}
{{{98-7-N=49}}}
{{{-N=49-98+7}}}
{{{N=98-49-7}}}
{{{highlight(N=42)}}}
Forty-Two sweets originally in the bag.