Question 526691
Let {{{ a }}} = Mary's age now
{{{ a + 1 }}} = Mary's age next year
Let {{{ b }}} = Mary's Mother's age now
{{{ b + 1 }}} = Mary's Mother's age next year
given:
(1) {{{ a = (1/6)*b }}}
(2) {{{ a + 1 = (1/5)*( b + 1 ) }}}
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(1) {{{ b = 6a }}}
and
(2) {{{ 5*( a + 1 ) = b + 1 }}}
(2) {{{ 5a + 5 = b + 1 }}}
(2) {{{ b - 5a = 4 }}}
Substitute (1) into (2)
(2) {{{ 6a - 5a = 4 }}}
(2) {{{ a = 4 }}}
and
(1) {{{ b = 6a }}}
(1) {{{ b = 6*4 }}}
(1) {{{ b = 24 }}}
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Mary is 4 now, and her Mother is 24
Let {{{ y }}} = the number of years from now when
Mary's age will be 1/3 of her mother's
{{{ a + y = (1/3)*( b + y ) }}}
{{{ 4 + y = (1/3)*(24 + y ) }}}
{{{ 3*( 4 + y ) = 24 + y }}}
{{{ 12 + 3y = 24 + y }}}
{{{ 3y - y = 24 - 12 }}}
{{{ 2y = 12 }}}
{{{ y = 6 }}}
In 6 years, Mary's age will be 1/3 her Mother's
check answer:
In 6 years, Mary will be 10
In 6 years Mother will be 30
Mary will be  1/3 her Mother's age