Question 1111879
Let {{{ a }}} = Mrs. Chen's age now.
Let {{{ b }}} = age of eldest child now
Let {{{ c }}} = age of middle child now
Let {{{ d }}} = age of youngest child now
--------------------------------------
(1) {{{ a - b = 20 }}}
( the difference in their ages will always be 20 yrs )
(2) {{{ a - c = 22 }}}
(3) {{{ a - d = 26 }}}
(4) {{{ ( a + b + c + d ) / 4 = 39 }}}
---------------------------------
(1) {{{ b = a - 20 }}}
(2) {{{ c = a - 22 }}}
(3) {{{ d = a - 26 }}}
By substitution:
(4) {{{ ( a + a - 20 + a - 22 + a - 26 ) / 4 = 39 }}}
(4) {{{ 4a - 68 ) / 4 = 39 }}}
(4) {{{ 4a - 68 = 156 }}}
(4) {{{ 4a = 224 }}}
(4) {{{ a = 56 }}}
and
(1) {{{ b = a - 20 }}}
(1) {{{ b = 56 - 20 }}}
(1) {{{ b = 36 }}}
and
(2) {{{ c = a - 22 }}}
(2) {{{ c = 56 - 22 }}}
(2) {{{ c = 34 }}}
and
(3) {{{ d = a - 26 }}}
(3) {{{ d = 56 - 26 }}}
(3) {{{ d = 30 }}}
--------------------------
Their ages are:
56, 36, 34, and 30
---------------------------
check:
 {{{ ( a + b + c + d ) / 4 = 39 }}}
{{{ ( 56 + 36 + 34 + 30 ) / 4 = 39 }}}
{{{ 156/4 = 39 }}}
{{{ 156 = 156 }}}
OK