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Question 635740: The sum of the digit of a three digit number is 12.If the digits are reversed the number are increased by 495 but reversing only of the ten’s and unit digits increases the number by 36.The number is:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The sum of the digit of a three digit number is 12.
If the digits are reversed the number are increased by 495
but reversing only of the ten’s and unit digits increases the number by 36.
The number is:
:
Let a = 100's digit
Let b = 10's digit
Let c = the units
Then
100a + 10b + c = "the number"
:
Write an equation for each statement, combine and simplify:
:
"The sum of the digit of a three digit number is 12."
a + b + c = 12
:
"If the digits are reversed the number are increased by 495"
100a + 10b + c = 100c + 10b + a - 495
100a - a + 10b - 10b = 100c - c - 495
99a = 99c - 495
divide thru by 99
a = c - 5
:
"but reversing only of the ten’s and unit digits increases the number by 36."
100a + 10b + c = 100a +10c + b - 36
100a - 100a + 10b - b = 10c - c - 36
9b = 9c - 36
simplify, divide by 9
b = c - 4
:
Back to the 1st equation
a + b + c = 12
replace a with (c-5); replace b with (c-4)
c-5 + (c-4) + c = 12
3c - 9 = 12
3c = 12 + 9
3c = 21
c = 21/3
c = 7
:
You should be able to find a and b, and create the original number
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