Question 881803
Let {{{ k }}} = Kate's age now
{{{ 50 }}} = her father's age now
Kate's father is 50 years old. Kate is 24 years old now.
The difference in their ages will never change
{{{ 50 - 24 = 26 }}}
So, I can say
{{{ f - k = 26 }}}
{{{ k = f - 26 }}}
Let {{{ n }}} = the number of years ago that
Kate's father was 3 times as old as her
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{{{ f50- n = 3*( k - n ) }}}
By substitution:
{{{ 50 - n = 3*( 50 - 26 - n ) }}}
{{{ 50- n = 3*50 - 78 - 3n }}}
{{{ 50 - n = 150 - 78 - 3n }}}
{{{ 3n - n = 150 - 78 - 50 }}}
{{{ 2n = 22 }}}
{{{ n = 11 }}}
11 years ago Kate's father was 3 times her age
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check:
11 years ago, father was {{{ 50 - 11 = 39 }}}
and, 11 years ago,
{{{ 39 = 3*k }}}
{{{ k = 13 }}}
The difference in their ages was:
{{{ 39 - 13 = 26 }}}
OK