SOLUTION: The tens digit of a number exceeds the units digit by 2. The sum of the digits is 1/7 of the number. What is the number?

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Question 88159: The tens digit of a number exceeds the units digit by 2. The sum of the digits is 1/7 of the number. What is the number?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be written as xy where x is the number of tens and y is the number of units.

Mathematically, the number is 10x+y

So, +x-y+=+2+ --1
and +x%2By+=+%281%2F7%29%2810x%2By%29+ --2

Simplifying eq2:
+7%28x%2By%29+=+10x%2By+
+7x%2B7y+=+10x%2By+
+6y+=+3x+
or +2y+=+x+

--1 is +x-y+=+2+ which then becomes +2y-y+=+2+
+y+=+2+

so using +2y+=+x+ and knowing that y=2, we get x=4

--> number is 42


cheers
Jon.