Question 611089
Let {{{ a }}} = my age now
Let {{{ b }}} = your age now
The difference in our ages will always be the same
That difference is {{{ a - b }}} ( I am older )
I was your age {{{ a - b }}} years ago, so I was
{{{ a - ( a - b ) }}} years old then.
You were {{{ b - (a - b) = 2b - a }}} years old then.
given:
(1) {{{ a = 2*( 2b - a ) }}}
(2) {{{ a + b = 42 }}}
-----------------------
(1) {{{ a = 4b - 2a }}}
(1) {{{ 3a = 4b }}}
(1) {{{ b = (3/4)*a }}}
By substitution:
(2) {{{ a + (3/4)*a = 42 }}}
(2) {{{ (7/4)*a = 42 }}}
(2) {{{ a = (4/7)*42 }}}
(2) {{{ a = 24 }}}
and, since
(2) {{{ a + b = 42 }}}
(2) {{{ b = 42 - 24 }}}
(2) {{{ b = 18 }}}
I am 24