SOLUTION: The tens' digit of a two didgit number is 3 more than the units' digit. The number is 8 more than 6 times the sum of the didgits. Find the number.

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Question 126290: The tens' digit of a two didgit number is 3 more than the units' digit. The number is 8 more than 6 times the sum of the didgits. Find the number.
Answer by solver91311(24713) About Me  (Show Source):
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If the tens digit is x and the ones digit is y, then we can say the number, n, is given by n=10x%2By. We also know that x=y%2B3 and n=6%28x%2By%29%2B8.

We can say that 10x%2By=6%28x%2By%29%2B8 and then substitute the fact that x=y%2B3

10%28y%2B3%29%2By=6%28%28y%2B3%29%2By%29%2B8
10y%2B30%2By=6y%2B18%2B6y%2B8
11y%2B30=12y%2B26
-y=-4
y=4

Which tells us that the ones digit is 4. From x=y%2B3 we can tell that the tens digit must be 7. Hence the number is 74.

Check the answer.

7=4%2B3
7%2B4=11, 11%2A6=66, 66%2B8=74. Answer checks.