Question 697161
Let {{{ a }}} = the Man's age now
Let {{{ b }}} = his Sister's age now
given:
(1) {{{ a + b = 97 }}}
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 }}}
{{{ 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 }}}
{{{ a = (4/3)*b }}}
Substitute this into (1)
(1) {{{ (4/3)*b + b = 97 }}}
(1) {{{ (7/3)*b = 97 }}}
(1) {{{ b = (3/7)*97 }}}
(1) {{{ b = 41.5714 }}}
and
{{{ a = (4/3)*b }}}
{{{ a = (4/3)*(3/7)*97 }}}
{{{ a = (4/7)*97 }}}
{{{ a = 55.4286 }}}{
The man is 55 and 5 months
His Sister is 41 and 7 months
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check:
{{{ 55.4286 - 41.5714 = 13.8572 }}}
When the man was {{{ 41.5714 }}}, his Sister was
{{{ 41.5714 - 13.8572 = 27.7142 }}}
The Man is twice this age
{{{ 2*27.7142 = 55.4284 }}}
Looks close enough