Question 884192
Let {{{ b }}} = brother's age now
Let {{{ s }}} = sister's age now
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(1) {{{ b = s + 3 }}}
(2) {{{ ( b  - 5 ) / ( s - 5 ) = 4/3 }}}
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(2) {{{ 3*( b - 5 ) = 4*( s - 5 ) }}}
(2) {{{ 3b - 15 = 4s - 20 }}}
(2) {{{ 3b - 4s = -5 }}}
and
(1) {{{ b - s = 3 }}}
Multiply both sides of (1) by {{{ 3 }}}
and subtract (2) from (1)
(1) {{{ 3b - 3s = 9 }}}
(2) {{{ -3b + 4s = 5 }}}
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{{{ s = 14 }}}
and, since
(1) {{{ b = s + 3 }}}
(1) {{{ b = 14 + 3 }}}
(1) {{{ b = 17 }}}
The sister is 14 and the brother is 17
check:
(2) {{{ ( 17  - 5 ) / ( 14 - 5 ) = 4/3 }}}
(2) {{{ 12 / 9 = 4/3 }}}
(2) {{{ 4/3 = 4/3 }}}
OK