Question 474228
Let {{{a}}} = Man's present age
Let {{{b}}} = Grandmother's present age
{{{ a - 18 }}} = Man's age 18 years ago
{{{ b - 18 }}} = Gradmother's age 18 years ago
given:
(1) {{{ a + b = 102 }}}
(2) {{{ b - 18 = 10*(a - 18) }}}
------------------------
(2) {{{ b - 18 = 10a - 180 }}}
(2) {{{ 10a - b = 180 - 18 }}}
(2) {{{ 10a - b = 162 }}}
Add (2) to (1)
(2) {{{ 10a - b = 162 }}}
(1) {{{ a + b = 102 }}}
{{{ 11a = 264 }}}
{{{ a = 24 }}}
And, from (1),
{{{ a + b = 102 }}}
{{{ 24 + b = 102 }}}
{{{ b = 78 }}}
The man is 24 and the Grandmother is 78
-------------
check:
(2) {{{ b - 18 = 10*(a - 18) }}}
(2) {{{ 78 - 18 = 10*(24 - 18) }}}
(2) {{{ 60 = 60 }}}
OK