Question 770096
Let {{{ a }}} = Jack's age
Let {{{ b }}} = John's age
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{{{ a + b = 49 }}}
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The difference in their ages always
stays the same, {{{ a - b }}}
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Starting at the end of the problem,
" when Jack was as old as John is now "
So Jack's age was {{{ b }}}
John had to have been {{{ b - ( a - b ) = 2b - a }}}
at that time
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It says that Jack is now twice that age, so
{{{ a = 2*( 2b - a ) }}}
{{{ a = 4b - 2a }}}
{{{ 3a = 4b }}}
{{{ b = ( 3/4 )*a }}}
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By substitution:
{{{ a + b = 49 }}}
{{{ a + (3/4)*a = 49 }}}
{{{ (7/4)*a = 49 }}}
{{{ a = (4/7)*49 }}}
{{{ a = 28 }}}
and
{{{ a + b = 49 }}}
{{{ b = 21 }}}
Jack is 28 and John is 21
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check:
" when Jack was as old as John is now "
Jack was 21
John had to have been 7 years younger,
or 14
Jack's age now is twice that age, or 28
OK