<PRE><B>Question 1124174</B>
let the 3 digit number = 100a + 10b + c
:
If the first and third digits of a three-digit number are interchanged, the difference between the original number and the new one is 198.
(100a+10b+c) - (100c+b+a) = 198
100a + 10b + c - 100c - 10b - a = 198
Combine like terms
100a - a + 10b - 10b + c - 100c = 198
99a - 99c = 198
simplify, divide by 99
a - c = 2
:
If the first and second digits of the original are interchanged, the new one is 90 less than the original.
100a + 10b + c - (100b + 10a + c) = 90
100a - 10a + 10b - 100b + c - c = 90
90a - 90b = 90
divide by 90
a - b = 1
:
 The difference between the first and third digits is equal to the second digit.
a - c = b
: 
Find the original number.
looking at the 1st and 3rd simplified equations we can see that b=2
Find a
a - 2 = 1
a = 3
and
3 - c = 2
c = 1
the original number: 321
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