SOLUTION: The sum of a the digits of a three digit number is 18. If the digits are reversed, the new number is the same as the original number. The units digit is one less than twice the te

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Question 994025: The sum of a the digits of a three digit number is 18. If the digits are reversed, the new number is the
same as the original number. The units digit is one less than twice the tens digit. Find the number.
Please help. Thank you.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Reversing the digits of a three-digit number, the hundreds digit and the units digit exchange places.
So, if after reversing the digits, the new number is the same as the original number,
the hundreds digit must be the same as the units digit.
x= hundreds digit = units digit
y= tens digit
x%2By%2Bx=2x%2By= sum of the digits
"The sum of the digits of a three-digit number is 18" translates as
2x%2By=18 .
"The units digit is one less than twice the tens digit" translates as
x=2y-1 .
system%28x=2y-1%2C2x%2By=18%29--->system%28x=2y-1%2C2%282y-1%29%2By=18%29--->system%28x=2y-1%2C4y-2%2By=18%29--->system%28x=2y-1%2C5y-2=18%29--->system%28x=2y-1%2C5y=18%2B2%29--->system%28x=2y-1%2C5y=20%29--->system%28x=2y-1%2Cy=20%2F5%29--->system%28x=2y-1%2Cy=4%29--->system%28x=2%2A4-1%2Cy=4%29--->highlight%28system%28x=7%2Cy=4%29%29 .
So the number is highlight%28747%29 .