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Question 891368: if the first and third digits of a 3 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 bewtween 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 a = the 100's digit
let b = the 10's
let c = the units
then
100a+10b+c = the original number
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write an equation for each equation, simplify as much as possible.
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if the first and third digits of a 3 digit number are interchanged, the difference between the original number and the new one is 198.
100a + 10b + c - (100c + 10b +a) = 198
removing the brackets changes the signs
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
c = a - 2; use for substitution
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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
do the same here
100a - 10a + 10b - 100b + c - c = 90
90a - 90b = 90
divide by 90
a - b = 1
b = a - 1; use for substitution
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The difference between the first and third digits is equal to the second digit.
a - c = b
Replace replace c with (a-2); replace b with (a-1)
a - (a-2) = a - 1
a - a + 2 = a - 1
2 + 1 = a
a = 3
then using our equations replace a with 3
c = 3 -2
c = 1
and
b = 3 - 1
b = 2
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321 is the original number
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See if that works in the statement," If the first and second digits of the original are interchanged the new one is 90 less than the original
321 - 231 = 90
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