Question 713537
Let {{{ a }}} = A's age now
Let {{{ b }}} = B's age now
---------------------------
" when I was as old as you are "
That means when A's age was equal to {{{ b }}}
----------------
" as old as you were "
The difference in their ages is always {{{ a-b }}}
so, at that time, B was {{{ b -( a-b ) = 2b - a }}}
-----------------
" A says to B,"I am 5 times "
A's present age, which is {{{ a }}} is {{{ 5*( 2b - a ) }}}
so I can say
(1) {{{ a = 5*( 2b-a ) }}}
----------------------
" the sum of their present ages of A & B = 64 "
(2) {{{ a + b = 64 }}}
(2) {{{ a = 64 - b }}}
and
(1) {{{ a = 5*( 2b-a ) }}}
(1) {{{ a = 10b - 5a }}}
(1) {{{ 6a = 10b }}}
(1) {{{ a = (5/3)*b }}}
By substitution:
(1) {{{ 64 - b = (5/3)*b }}}
(1) {{{ (8/3)*b = 64 }}}
(1) {{{ b = (3/8)*64 }}}
(1) {{{ b = 24 }}}
and, since
(2) {{{ a = 64 - b }}}
(2) {{{ a = 64 - 24 }}}
(2) {{{ a = 40 }}}
A is 40 and B is 24
check:
" when I was as old as you are "
When A was 24, B had to be {{{ 24 -( 40 - 24 ) = 24 - 16 }}}
{{{ 24 - 16 = 8 }}}
"I am 5 times as old as you were"
A is {{{ 5*8 = 40 }}}
OK