Question 697171
Let {{{ a }}}  = the Man's age now
Let {{{ b }}}  = his Sister's age now
given:
(1) {{{ a + b = 91 }}}
When the Man's age was {{{ b }}} , the age his
Sister is now, how old was his Sister then?
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The separation in their ages will always be 
{{{ a - b }}}
( assuming the Man is older )
So, when the Man was  {{{ b }}} years old, his Sister
was 
{{{ b - ( a - b ) = b - a + b }}}
{{{ 2b - a }}}
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The man is now twice this age, so he is
{{{ 2*( 2b - a ) = 4b - 2a }}}
And, I can now say
{{{ a = 4b - 2a }}}
{{{ 3a = 4b }}}
{{{ b = ( 3/4)*a }}}
Substitute this into (1)
(1) {{{ a + b = 91 }}} 
(1) {{{ a + (3/4)*a = 91 }}}
(1) {{{ (7/4)*a = 91 }}} 
(1) {{{ a = (4/7)*91 }}}
(1) {{{ a = 52 }}} 
and, since
(1) {{{ a + b = 91 }}}
(1) {{{ 52 + b = 91 }}}
(1) {{{ b = 91 - 52 }}}
(1) {{{ b = 39 }}}
The man is 52
His Sister is 39
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check:
52 - 39 = 13, which is always
the difference in their ages
When the man was 39 , his Sister was 39 - 13 = 26 
The Man is twice this age, or 2*26 = 52
OK