Question 1031190
Let {{{ f }}} = father's age now
Let {{{ s }}} = his son's age now
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(1) {{{ f - 2 = 3*( s - 2 ) }}}
(2) {{{ 2*( f + 2 ) = 5*( s + 2 ) }}}
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(1) {{{ f - 2 = 3s - 6 }}}
(1) {{{ 3s - f = 4 }}}
and
(2) {{{ 2f + 4 = 5s + 10 }}}
(2) {{{ -5s + 2f = 6 }}}
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Multiply both sides of (1) by {{{ 2 }}}
and add the equations
(1) {{{ 6s - 2f = 8 }}}
(2) {{{ -5s + 2f = 6 }}}
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{{{ s = 14 }}}
and
(1) {{{ 3s - f = 4 }}}
(1) {{{ f = 3s - 4 }}}
(1) {{{ f = 3*14 - 4 }}}
(1) {{{ f = 38 }}}
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The son is 14 and the father is 38
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check:
(1) {{{ f - 2 = 3*( s - 2 ) }}}
(1) {{{ 38 - 2 = 3*( 14 - 2 ) }}}
(1) {{{ 36 = 3*12 }}}
(1) {{{ 36 = 36 }}}
OK
(2) {{{ 2*( f + 2 ) = 5*( s + 2 ) }}}
(2) {{{ 2*( 38 + 2 ) = 5*( 14 + 2 ) }}}
(2) {{{ 80 = 5*16 }}}
(2) {{{ 80 = 80 }}}
OK