Question 459943


Tlet’s two -digits number be: {{{xy}}}

{{{x }}}= the 10's digit
{{{y }}}= units digit

The original number is: {{{10x + y}}}

given: 

the digits of a two-digit number are reversed, the new number is {{{9}}}{{{ more}}}
 than the original number

the sum of the digits of the original number is 11: {{{x + y = 11}}}.....

you will have:

{{{10y + x = 10x + y + 9}}}

{{{10y - y = 10x - x + 9}}}

{{{9y = 9x + 9}}}.........both sides divide by {{{9}}}

{{{y = x + 1}}}


Replace {{{y }}}with {{{(x+1)}}} and plug it in  {{{x + y = 11}}}

{{{x + x + 1 = 11}}}

{{{2x = 10}}}

{{{x = 5}}}......the 10's digit

then, the units digit will be

{{{y = 5 + 1}}}

{{{y = 6}}}

and the original number is: {{{10x + y=10*5+6=56}}}

if the digits of a two-digit number are reversed, we will have a number {{{65}}}


{{{65-56=9}}}...so, the new number is {{{9}}}{{{ more}}}
 than the original number