Answer :
The original number is 34 .
The sum of its digits is (3 + 4) = 7 .
Reversing its digits makes it 43 . . . 9 more than 34.
How I did it: (There must be a much more elegant mathematical method)
There are only 6 possibilities for the original number.
They are . . .
16
25
34
43
52
61 .
Instead of trying to dream up a sophisticated equation,
I decided it was faster and easier to just go down the list
and look for one that worked.
The third one I tried worked.
The sum of its digits is (3 + 4) = 7 .
Reversing its digits makes it 43 . . . 9 more than 34.
How I did it: (There must be a much more elegant mathematical method)
There are only 6 possibilities for the original number.
They are . . .
16
25
34
43
52
61 .
Instead of trying to dream up a sophisticated equation,
I decided it was faster and easier to just go down the list
and look for one that worked.
The third one I tried worked.
Let the two numbers be x and y.
According to your question;
x + y = 7
10y + x = 10x + y + 9
By equation 1 ; x = 7-y
Substituting the value of x ;
10y + ( 7 -y) = 10(7-y) + y + 9
9y + 7 = 70 -10y + y + 9
9y + 7 = 70 - 9y + 9
=> 18y = 70 -7 + 9
=> 18y = 72
=> y = 4
Substituting for x ;
x = 7 - y
=> x = 7 -4
=> x = 3
Thus, x = 3 and y = 4;
=> The number is 34.
According to your question;
x + y = 7
10y + x = 10x + y + 9
By equation 1 ; x = 7-y
Substituting the value of x ;
10y + ( 7 -y) = 10(7-y) + y + 9
9y + 7 = 70 -10y + y + 9
9y + 7 = 70 - 9y + 9
=> 18y = 70 -7 + 9
=> 18y = 72
=> y = 4
Substituting for x ;
x = 7 - y
=> x = 7 -4
=> x = 3
Thus, x = 3 and y = 4;
=> The number is 34.
