Question 861331
Let {{{ g }}} = graces age now
Let {{{ c }}} = cousin's age now
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(1) {{{ g/c = 4/5 }}}
(2) {{{ ( g + 6 ) / ( c + 6 ) = 11/13 }}}
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(2) {{{ 13*( g + 6 ) = 11*( c + 6 ) }}}
(2) {{{ 13g + 78 = 11c + 66 }}}
(2) {{{ 11c - 13g = 12 }}}
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(1) {{{ 5g = 4c }}}
(1) {{{ g = ( 4/5 )*c }}}
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Substitute (1) into (2)
(2) {{{ 11c - 13*(4/5)*c = 12 }}}
(2) {{{ 55c - 52c = 60 }}}
(2) {{{ 3c = 60 }}}
(2) {{{ c = 20 }}}
and
(1) {{{ g = ( 4/5 )*20 }}}
(1) {{{ g = 16 }}}
Grace is 16
check:
(2) {{{ ( g + 6 ) / ( c + 6 ) = 11/13 }}}
(2) {{{ ( 16 + 6 ) / ( 20 + 6 ) = 11/13 }}}
(2) {{{ 22 / 26 = 11/13 }}}
(2) {{{ 11/13 = 11/13 }}}
OK