Question 1022139
Let {{{ s }}} =son's present age
Let {{{ f }}} = father's present age
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The difference in their ages is always
the same: {{{ f - s }}}
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His son replies" when I reach your age, you will be 68
When the son's age = {{{ f }}}, then the father's age
will be {{{ 68 }}}. Since the differnce in their ages
stays the same:
{{{ 68 - f = f - s }}}
(1) {{{ 2f - s = 68 }}}
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His father says "when i was your age, you were 2 years old.
The father's age was {{{ s }}}, and the son was {{{ 2 }}}
The difference in their ages stays the same:
{{{ s - 2 = f - s }}}
(2) {{{ -f + 2s = 2 }}}
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Multiply both sides of (2) by {{{ 2 }}} and
add the equations
(1) {{{ 2f - s = 68 }}}
(2) {{{ -2f + 4s = 4 }}}
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{{{ 3s = 72 }}}
{{{ s = 24 }}}
and
(2) {{{ -f + 2s = 2 }}}
(2) {{{ -f + 2*24 = 2 }}}
(2) {{{ f = 48 - 2 }}}
(2) {{{ f = 46 }}}
The father's present age is 46
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check:
{{{ f - s = 46 - 24 }}}
{{{ f - s = 22 }}}
His father says "when i was your age, you were 2 years old.
When the father was 24, the son was {{{ 24 - 22 = 2 }}}
OK
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His son replies" when I reach your age, you will be 68?
When the son is 46, the father will be {{{ 46 + 22 = 68 }}}
OK