Question 709318
Let {{{ m }}} = age of Mother 3 years ago
Let {{{ d }}} = age of Daughter 3 years ago
{{{ m + 3 }}} = mother's age now
{{{ d + 3 }}} = Daughter's age now
given:
(1) {{{ ( m + 3 ) + ( d + 3 ) = 44 }}}
(2) {{{ m*d = 192 }}}
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(1) {{{ m + d + 6 = 44 }}}
(1) {{{ m + d = 38 }}}
(1) {{{ m = 38 - d }}}
and
(2) {{{ ( 38 - d )*d = 192 }}}
(2) {{{ 38d - d^2 = 192 }}}
(2) {{{ -d^2 + 38d = 192 }}}
(2) {{{ d^2 - 38d = -192 }}}
(2) {{{ d^2 - 38d + (38/2)^2 = -192 + (38/2)^2 }}}
(2) {{{ d^2 - 38d + 361 = -192 + 361 }}}
(2) {{{ ( d - 19 )^2 = 169 }}}
(2) {{{ ( d - 19 )^2 = 13^2 }}}
Take the square root of both sides
(2) {{{ d - 19 = 13 }}}
(2) {{{ d = 32 }}}
and, since
(1) {{{ m = 38 - d }}}
(1) {{{ m = 38 - 32 }}}
(1) {{{ m = 6 }}}
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This didn't work because the Daughter is 32 ( 3 yrs ago ) 
and the Mother is 6 ( 3 yrs ago ). To make it right, just take the 
negative square root of {{{ 13^2 }}} a few steps aback
(2) {{{ ( d - 19 )^2 = 13^2 }}}
(2) {{{ d - 19 = -13 }}}
(2) {{{ d = 19 - 13 }}}
(2) {{{ d = 6 }}}
Now it works out- the Daughter was 6 three years ago,
so now the Daughter is 9 now.
check answer:
(2) {{{  m*d = 192 }}}
(2) {{{  32*6 = 192 }}}
(2) {{{ 192 = 192 }}}
OK