Question 835040
Let {{{ f }}} = father's's age now
Let {{{ s }}} = son's age now
Let {{{ d }}} = daughter's age now
----------------------------
(1) {{{ s = d + 3 }}}
(2) {{{ f + 1 = 6d }}}
(3) {{{ f + 10 = ( s+10 ) + ( d+10 ) + 14 }}}
--------------------------------------
(2) {{{ f = 6d - 1 }}}
and
(3) {{{ f + 10 =  s+10 +  d+10 + 14 }}}
(3) {{{ f + 10 = s + d + 34 }}}
(3) {{{ f = s + d + 24 }}}
-----------------------
Substitute (1) and (2) into (3)
(3) {{{ 6d - 1 = d + 3 + d + 24 }}}
(3) {{{ 6d - 1 = 2d + 27 }}}
(3) {{{ 4d = 28 }}}
(3) {{{ d = 7 }}}
----------------
(2) {{{ f = 6d - 1 }}}
(2) {{{ f = 6*7 - 1 }}}
(2) {{{ f = 41 }}}
--------------
(1) {{{ s = d + 3 }}}
(1) {{{ s = 7 + 3 }}}
(1) {{{ s = 10 }}}
---------------
The father's age is 41
check:
(3) {{{ f + 10 = ( s+10 ) + ( d+10 ) + 14 }}}
(3) {{{ 41 + 10 = ( 10+10 ) + ( 7+10 ) + 14 }}}
(3) {{{ 51 = 20 + 17 + 14 }}}
(3) {{{ 51 - 51 }}}
OK
---------
(2) {{{ f + 1 = 6d }}}
(2) {{{ 41 + 1 = 6*7 }}}
(2) {{{ 42 = 42 }}}
OK
--------
(1) {{{ s = d + 3 }}}
(1) {{{ 10 = 7 + 3 }}}
(1) {{{ 10 = 10 }}}
OK