Question 883776
Let {{{ a }}} = the present age of the son
Let {{{ b }}} = the present age of the father
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Note that the difference in their ages will
never change: it is {{{ b - a }}}
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The father says: " when I was as old as you are "
That means when the father's age was {{{ a }}}
Back then, the son's age must have been:
{{{ a - ( b - a ) = 2a - b }}}
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The father says " I am 7 times as old as you were
when I was as old as you are ", so
(1) {{{ b = 7*( 2a - b ) }}}
also given:
(2) {{{ a + b = 110 }}}
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(1) {{{ b = 14a - 7b }}}
(1) {{{ 14a = 8b }}}
(1) {{{ 7a = 4b }}}
(1) {{{ a = ( 4/7 )*b }}}
By substitution:
(2) {{{ ( 4/7 )*b + b = 110 }}}
(2) {{{ ( 11/7 )*b = 110 }}}
(2) {{{ ( 1/7 )*b = 10 }}}
(2) {{{ b = 70 }}}
and, since
(2) {{{ a + b = 110 }}}
(2) {{{ a = 40 }}}
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The father is 70 and the son is 40
check:
The difference {{{ b- a = 30 }}}
{{{ a - ( b - a ) = 40 - 30 }}}
{{{ 40 - 30 = 10 }}}
(1) {{{ b = 7*( 2a - b ) }}}
(1) {{{ b = 7*10 }}}
(1) {{{ b = 70 }}}
OK