Question 1153947
Let {{{ a }}} = the age of the youngest
Let {{{ b }}} = the age of the middle child
Let {{{ c }}} = the age of the oldest
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(1) {{{ a + b + c = 50 }}}
(2) {{{ a = (1/2)*c }}}
(3) {{{ c - 10 = 7*( a - 10 ) }}}
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(2) {{{ c = 2a }}}
(3) {{{ 2a - 10 = 7*( a - 10 ) }}}
(3) {{{ 2a - 10 = 7a - 70 }}}
(3) {{{ 5a = 60 }}}
(3) {{{ a = 12 }}}
and
(2) {{{ c = 2a }}}
(2) {{{ c = 2*12 }}}
(2) {{{ c = 24 }}}
and
(1) {{{ a + b + c = 50 }}}
(1) {{{ 12 + b + 24 = 50 }}}
(1) {{{ b + 36 = 50 }}}
(1) {{{ b = 14 }}}
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Ten years ago, their ages were:
Youngest: {{{ 12 - 10 = 2 }}}
Middle: {{{ 14 - 10 = 4 }}}
Oldest: {{{ 24 - 10 = 14 }}}
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check:
(3) {{{ c - 10 = 7*( a - 10 ) }}}
(3) {{{ 24 - 10 = 7*( 12 - 10 ) }}}
(3) {{{ 14 = 7*2 }}}
OK