Question 876577
Let {{{ f }}} = father's age now
Let {{{ s }}} = son's age now
------------------------
{{{ f - 5 }}} = father's age 5 yrs ago
{{{ s - 5 }}} = son's age 5 yrs ago
-----------------------------
{{{ f + 5 }}} = father's age in 5 yrs
{{{ s + 5 }}} = son's age in 5 yrs
----------------------------
(1) {{{ f - 5 = 7*( s - 5 ) }}}
(2) {{{ f + 5 = 3*( s + 5 ) }}}
-----------------------
(1) {{{ f - 5 = 7s - 35 }}}
(1) {{{ 7s - f = 30 }}}
-------------------
(2) {{{ f + 5 = 3s + 15 }}}
(2) {{{ 3s - f = -10 }}}
-------------------
Subtract (2) from (1)
(1) {{{ 7s - f = 30 }}}
(2) {{{ -3s + f = 10 }}}
{{{ 4s = 40 }}}
{{{ s = 10}}}
and
(1) {{{ f - 5 = 7*( s - 5 ) }}}
(1) {{{ f - 5 = 7*( 10 - 5 ) }}}
(1) {{{ f - 5 = 7*5 }}}
(1) {{{ f = 40 }}}
--------------
The father is 40 and the son is 10
This checks out if you read back
through the problem