Question 174725
Call the units digit {{{n}}}
Call the tens digit {{{m}}}
Given:
{{{n + m = 10}}}
The actual value of the number is
{{{10m + n}}}
The value of the number with the digits reversed is
{{{10n + m}}}
Given:
{{{10n + m = 10m + n + 72}}}
(1) {{{9n - 9m = 72}}}
(2) {{{n + m = 10}}}
Multiply both sides of (2) by {{{9}}} and add to (1)
(1) {{{9n - 9m = 72}}}
(2) {{{9n + 9m = 90}}}
(3) {{{18n = 162}}}
{{{n = 9}}}
{{{n + m = 10}}}
{{{m = 10 - 9}}}
{{{m = 1}}}
The original number is 19
check:
{{{91 = 19 + 72}}}
{{{91 = 91}}}
OK