Question 625355
Let {{{ m }}} = Mother's age now
Let {{{ d }}} = daughter's age now
given:
(1) {{{ d/m = 7/20 }}}
(2) {{{ m - 4 = 6*( d - 4 ) }}}
---------------------
(1) {{{ 20d = 7m }}}
(1) {{{ m = (20/7)*d }}}
Substitute (1) into (2)
(2) {{{ (20/7)*d - 4 = 6*( d - 4 ) }}}
Multiply both sides by {{{ 7 }}}
(2) {{{ 20d - 28 = 42*( d - 4 ) }}}
(2) {{{ 20d - 28 = 42d - 168 ) }}}
(2) {{{ 22d = 168 - 28 }}}
(2) {{{ 22d = 140 }}}
(2) {{{ d = 70/11 }}}
and, since
(1) {{{ m = (20/7)*d }}}
(1) {{{ m = (20/7)*(70/11) }}}
(1) {{{ m = 18.2 }}}
The Mother is 18. Check my math- these types of
problems usually have whole number answers.
check answer:
(2) {{{ m - 4 = 6*( d - 4 ) }}}
(2) {{{ 200/11 - 4 = 6*( 70/11 - 4 ) }}}
Multiply both sides by {{{ 11 }}}
(2) {{{ 200 - 44 = 420 - 264 }}}
(2) {{{ 156 = 156 }}}
It checks