Question 526843
Let {{{a}}} = my age now
Let {{{b}}} = your age now
Note that the difference in our ages
will always be {{{ a - b }}}
( I think I am older than you )
----------------------
given:
When my age was your age, then you
must have been {{{ b - (a-b) = 2b - a }}}
{{{ a = 2*( 2b - a ) }}}
{{{ a = 4b - 2a }}}
{{{ 3a = 4b }}}
(1) {{{ b = (3/4)*a }}}
and
When your age becomes {{{a}}}, then I
will be {{{ a + (a-b) = 2a - b }}}
{{{ a + 2a - b = 27 }}}
(2) {{{ 3a - b = 27 }}}
Substitute (1) into (2)
(2) {{{ 3a - (3/4)*a = 27 }}}
(2) {{{ 12a - 3a = 108 }}}
(2) {{{ 9a = 108 }}}
(2) {{{ a = 12 }}}
I am 12
check:
(1) {{{ b = (3/4)*a }}}
(1) {{{ b = (3/4)*12 }}}
(1) {{{ b = 9 }}
(2) {{{ 3a - b = 27 }}}
(2) {{{ 3*12 - 9 = 27 }}}
(2) {{{ 36 - 9 = 27 }}}
(2) {{{ 27 = 27 }}}
OK