Question 561142
Let {{{ m }}} = Mother's age now
Let {{{ d }}} = Daughter's age now
{{{ m + 7 }}} = Mother's age in 7 years
{{{ d + 7 }}} = Daughter's age in 7 years
given:
(1) {{{ m = d + 20 }}}
(2) {{{ m + 7 = 3*( d + 7 ) }}}
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(2) {{{ m + 7 = 3d + 21 }}}
(2) {{{ m - 3d = 14 }}}
and
(1) {{{ m - d = 20 }}}
Subtract (2) from (1)
(1) {{{ m - d = 20 }}}
(2) {{{ -m + 3d = -14 }}}
{{{ 2d = 6 }}}
{{{ d = 3 }}}
and, since
(1) {{{ m = d + 20 }}}
(1) {{{ m = 3 + 20 }}}
(1) {{{ m = 23 }}}
The Mother is 23 and the Daughter is 3
check:
(2) {{{ m + 7 = 3*( d + 7 ) }}}
(2) {{{ 23 + 7 = 3*( 3 + 7 ) }}}
(2) {{{ 30 = 30 }}}
OK