Question 984046
Let {{{s }}} = Samuel's age now
Let {{{ b }}} = brother's age now
(1) {{{ s = (1/2)*b }}}
(2) {{{ s + 7 = (2/3)*( b + 7 ) }}}
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substitute (1) into (2)
(2) {{{ (1/2)*b + 7 = (2/3)*( b + 7 ) }}}
Multiply both sides by {{{ 6 }}}
(2) {{{ 3b + 42 = 4*( b + 7 ) }}}
(2) {{{ 3b + 42 = 4b + 28 }}}
(2) {{{ b = 42 - 28 }}}
(2) {{{ b = 14 }}}
and
(1) {{{ s = (1/2)*14 }}}
(1) {{{ s = 7 }}}
Samuel is 7
His brother is 14
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check:
(2) {{{ s + 7 = (2/3)*( b + 7 ) }}}
(2) {{{ 7 + 7 = (2/3)*( 14 + 7 ) }}}
(2) {{{ 14 = (2/3)*21 }}}
(2) {{{ 42 = 2*21 }}}
(2)  {{{ 42 = 42 }}}
OK