Question 786274
Let {{{ m }}} = mother's age now
Let {{{ d }}} = daughter's age now
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{{{ d + 2 }}} = daughter's age {{{ 2 }}} yrs from now
{{{ 2*( d + 2 ) }}} = twice daughter's age {{{ 2 }}} yrs from now
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{{{ m + d = 55 }}}
{{{ -d = m - 55 }}}
{{{ m - d = m + m - 55 }}}
{{{ m - d = 2m - 55 }}}
The difference in their ages will always be {{{ 55 }}} yrs
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When the mother was {{{ 2*( d + 2 ) }}}, the daughter
was  {{{ 2*( d + 2 ) - ( 2m - 55 ) }}}
also given:
{{{ m = 3*( 2*( d+2 ) - ( 2m - 55 ) ) }}}
{{{ m = 3*( 2d + 4 - 2m + 55 ) }}}
{{{ m = 3*( 2d - 2m + 59 ) }}}
{{{ m = 6d - 6m + 177 }}}
{{{ 7m = 6d + 177 }}}
and, since {{{ m + d = 55 }}},
{{{ 7m = 6*( 55 - m ) + 177 }}}
{{{ 7m = 330 - 6m + 177 }}}
{{{ 13m = 507 }}}
{{{ m = 39 }}}
and
{{{ d = 55 - m }}}
{{{ d = 16 }}}
The woman is 39 and the daughter is 16
check:
2 yrs from now, daughter is 18
twice that is 36
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When the mother was 36, daughter was 13
Three time 13 is 39
OK