Question 1111128
Let {{{ a }}} = father's age now
Let {{{ b }}} = son's age now
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(1) {{{ ( a - 2 ) / ( b - 2 ) = 10/1 }}}
(2) {{{ a + 4 = 4*( b + 4 ) }}}
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(1) {{{ a - 2 = 10*( b - 2 ) }}}
(1) {{{ a - 2 = 10b - 20 }}}
(1) {{{ -a + 10b = 18 }}}
and
(2) {{{ a + 4 = 4b + 16 }}}
(2) {{{ a - 4b = 12 }}}
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Add (1) and (2)
(1) {{{ -a + 10b = 18 }}}
(2) {{{ a - 4b = 12 }}}
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{{{ 6b = 30 }}}
{{{ b = 5 }}}
and
(2) {{{ a - 4b = 12 }}}
(2) {{{ a - 4*5 = 12 }}}
(2) {{{ a = 12 + 20 }}}
(2) {{{ a = 32 }}}
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{{{ a - b = 32 - 5 }}}
{{{ a - b = 27 }}}
The difference in their ages is 27
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check:
(1) {{{ ( a - 2 ) / ( b - 2 ) = 10 }}}
(1) {{{ ( 32 - 2 ) / ( 5 - 2 ) = 10 }}}
(1) {{{ 30 / 3 = 10 }}}
(1) {{{ 10 = 10 }}}
and
(2) {{{ a + 4 = 4*( b + 4 ) }}}
(2) {{{ 32 + 4 = 4*( 5 + 4 ) }}}
(2) {{{ 36 = 4*9 }}}
(2) {{{ 36 = 36 }}}
OK