Question 376455
The original number: 100x + 10y + z

The sum of three digits is 5.
x + y + z = 5
:
 The first and last digits are the same.
x = z
therefore we can write the number
100x + 10y + x
:
 If the middle digit is exchanged with the first digit, the new number is 90 less than the original number.
:
100x + 10y + x = 100y + 10x + x + 90
combine like terms
100x - 10x + x - x = 100y - 10y + 90
90x = 90y + 90
simplify, divide by 90
x = y + 1
:
x + y + z = 5
Since 1st and last digit are the same
(y+1) + y + (y+1) = 5
3y = 5 - 2
y = 1
then, x and z = 2
:
212 is the original number
:
:
Check in the statement;
If the middle digit is exchanged with the first digit, the new number is 90 less than the original number.
212 = 122 + 90; confirms our solution