Question 638254
Let {{{ m }}} = Mary's age now
Let {{{ d }}} = Daughter's age now
given:
(1) {{{ m = 4d }}}
(2) {{{ ( m - 4 )*( d - 4 ) = 40 }}}
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Substitute (1) into (2)
(2) {{{ ( 4d - 4 )*( d - 4 ) = 40 }}}
(2) {{{ 4* ( d - 1 )*( d - 4 ) = 40 }}}
(2) {{{  ( d - 1 )*( d - 4 ) = 10 }}}
(2) {{{ d^2 -d - 4d + 4 = 10 }}}
(2) {{{ d^2 - 5d - 6 = 0 }}}
(2) {{{ ( d - 6 )*( d + 1 ) = 0 }}}
{{{ d = 6 }}}
{{{ d = -1 }}}
Daughter's  age must be positive, so
the Daughter is 6
and, since
(1) {{{ m = 4d }}}
(1) {{{ m = 4*6 }}}
(1) {{{ m = 24 }}}
The Mother is 24
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check answers
(2) {{{ ( m - 4 )*( d - 4 ) = 40 }}}
(2) {{{ ( 24 - 4 )*( 6 - 4 ) = 40 }}} 
(2) {{{ 20*2 = 40 }}}
(2) {{{ 40 = 40 }}}
OK