Question 803222
Let the tens digit = {{{ t }}}
Let the units digit = {{{ u }}}
------------
'(1) {{{ t + u = 9 }}}
(2) {{{ 10u + t = 2*( 10t + u ) + 18 }}}
-------------------------------
(2) {{{ 10u  + t = 20t + 2u + 18 }}}
(2) {{{ 10u - 2u + t - 20t = 18 }}}
(2) {{{ 8u - 19t = 18 }}}
and, since
'(1) {{{ t + u = 9 }}}
(1) {{{ u = 9 - t }}}
By substitution:
(2) {{{ 8*( 9 - t ) - 19t = 18 }}}
(2) {{{ 72 - 8t - 19t = 18 }}}
(2) {{{ -27t = -54 }}}
(2) {{{ t = 2 }}}
and
(1) {{{ u = 9 - t }}}
(1) {{{ u = 7 }}}
The original number is 27
----------------------
check:
Reverse digits: {{{ 72 }}}
{{{ 72 = 2*( 27 ) + 18 }}}
{{{ 72 = 54 + 18 }}}
{{{ 72 = 72 }}}
OK