Question 1059171
Let m = mother's age now
and  d = daughter's age now

"the sum of the ages of a mother and her daughter is 52"
gives
  {{{ m + d = 52 }}}

and
"8 years ago, the mother was 8 times as old as her daughter" 
gives
{{{ m-8 = 8*(d-8) }}} 

The first equation gives us {{{ d = 52-m }}} and now we can substitute "52-m" for "d" in the 2nd equation.

{{{ m-8 = 8*((52-m) - 8) }}} 
{{{  m -8 = 352 - 8m }}}

Can you solve for m?