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Question 1124174: 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. If the first and second digits of the original are interchanged, the new one is 90 less than the original. The difference between the first and third digits is equal to the second digit. Find the original number.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! let the 3 digit number = 100a + 10b + c
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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
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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
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The difference between the first and third digits is equal to the second digit.
a - c = b
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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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