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Question 228598: The sum of the digits of a three-digit number is 18. The ten's digit is 2 more than the unit's digit. If the digits are reversed, the resulting number is 396 less than the original number. Find the original number.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The sum of the digits of a three-digit number is 18.
The ten's digit is 2 more than the unit's digit.
If the digits are reversed, the resulting number is 396 less than the original number.
Find the original number.
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Three digits, x & y & z
the number: 100x + 10y + z
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"The sum of the digits of a three-digit number is 18."
x + Y + z = 18
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" The ten's digit is 2 more than the unit's digit.
y = z + 2
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"If the digits are reversed, the resulting number is 396 less than the original number."
original number - 396 = reversed number
100x + 10y + z - 396 = 100z + 10y + x
Group like terms and combine
100x - x + 10y - 10y = 100z - z + 396
99x = 99z + 396
Simplify, divide equation by 99
x = z + 4
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Find the original number.
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Using the equation x + y + z = 18, replace y and x
(z+4) + (z + 2) + z = 18
3z + 6 = 18
3z = 18 - 6
3z = 12
z = 4
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I'll let you find x and y using the equations derived from the statements
Construct the number using 100x + 10y + z, check in last statement
Any questions, ankor@att.net
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