Question 1130158
Let {{{ a }}} = the man's age now
Let {{{ b }}} = his wife's age now
Let {{{ c }}} = his son's age now
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(1) {{{ a = b + 8 }}}
(2) {{{ a = 6c }}}
(3) {{{ b - c = (4/5)*( a - c ) }}}
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(1) {{{ b = a - 8 }}}
(1) {{{ b = 6c - 8 }}}
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By substitution:
(3) {{{ 6c - 8 - c = (4/5)*( 6c - c ) }}}
(3) {{{ 5*( 5c - 8 ) = 4*5c }}}
(3) {{{ 25c - 40 = 20c }}}
(3) {{{ 5c = 40 }}}
(3) {{{ c = 8 }}}
The son is 8
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check:
(2) {{{ a = 6c }}}
(2) {{{ a = 48 }}}
and
(1) {{{ b = 6*8 - 8 }}}
(1) {{{ b = 48 - 8 }}}
(1) {{{ b = 40 }}}
and
(3) {{{ b - c = (4/5)*( a - c ) }}}
(3) {{{ 40 - 8 = (4/5)*( 48 - 8 ) }}}
(3) {{{ 32 = (4/5)*40 }}}
(3) {{{ 32 = 32 }}}
OK