SOLUTION: A number is 7 times the sum of its digits. If the digits are reversed, the new number is 30 less than twice the original.

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Question 1082461: A number is 7 times the sum of its digits. If the digits are reversed, the new number is 30 less than twice the original.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A and B are integers from 0-9.
Let the original number be 10A%2BB.
The sum of its digits would be A%2BB.
Digits reversed would be 10B%2BA.
So,
10A%2BB=7%28A%2BB%29
10A%2BB=7A%2B7B
3A=6B
1.A=2B
and
10B%2BA=2%2810A%2BB%29-30
10B%2BA=20A%2B2B-30
2.19A-8B=30
Substituting from 1 into 2,
19%282B%29-8B=30
38B-8B=30
30B=30
Solve for B, then use either equation to solve for A.