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Question 1169317: A three-digit number is such that the sum of the digits is 12. If the digits are reversed, the resulting number is 198 less than the original number. Also, the hundreds digit is equal to the sum of the ones digit and the tens digit. Find the original number.
Found 2 solutions by ankor@dixie-net.com, josgarithmetic:
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 digit
let c = the unite
then
100a + 10b + c = the original number
:
write an equation for each statement, simplify
:
A three-digit number is such that the sum of the digits is 12.
a + b + c = 12
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If the digits are reversed, the resulting number is 198 less than the original number.
100a + 10b + c = 100c + 10b + a + 198
Combine like terms on the left
100a - a + 10b - 10b + c - 100c = 198
99a - 99c = 198
simplify, divide by 99
a - c = 2
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Also, the hundreds digit is equal to the sum of the ones digit and the tens digit. Find the original number.
a = b + c
rewrite to
a - b - c = 0
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Use elimination on the 1st and last equations
a + b + c = 12
a - b - c = 0
---------------addition eliminates b and c, find a
2a = 12
a = 6
Replace a with 6 in the 2nd simplified equation
6 - c = 2
-c = 2 - 6
-c = -4
c = 4
find b
6 + b + 4 = 12
b = 12 - 10
b = 2
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the original number: 624
:
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Check in the statement
"If the digits are reversed, the resulting number is 198 less than the original number."
Subtract
624
426
----
198
Answer by josgarithmetic(39621)  (Show Source):
You can put this solution on YOUR website! h, t, u
hundreds, tens, ones
Description may first give  .
Some simplification:
.
.
After a few substitutions and algebra steps,
the number: 624
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