Question 1064162
{{{10a+b}}}= the number
{{{10b+a}}}= the result of reversing the digits
The clues in the problem translate into two equations:
{{{a+b=7}}}= the sum of the digits
{{{(10b+a)-(10a+b)=27}}}= the reversed number minus the original number
Solving the system:
Simplifying the second equation we get {{{b=a+3}}} :
{{{(10b+a)-(10a+b)=27}}}
{{{10b+a-10a-b=27}}}
{{{9b-9a=27}}}
{{{9(b-a)=27}}}
{{{b-a=27/9}}}
{{{b-a=3}}}
{{{b=a+3}}}
Substituting {{{a+3}}} for {{{b}}} in {{{a+b=7}}}
we get
{{{a+a+3=7}}}
{{{2a+3=7}}}
{{{2a=7-3}}}
{{{2a=4}}}
{{{a=4/2}}}
{{{a=2}}}
Substituting {{{2}}} for {{{a}}} in {{{b=a+3}}} we get
{{{b=2+3}}}
{{{b=5}}}
So, the number is {{{highlight(25)}}}