SOLUTION: A two-digit number has 3 in its unit digit. The sum of its digits is one-seventh of the number itself. What is the number?

Question 662642: A two-digit number has 3 in its unit digit. The sum of its digits is one-seventh of the number itself. What is the number?
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Sorry, thought I could cut corners and give you the quick answer. Here's the whole story.
Let n = tens digit
Let m = units digit
Then your whole number is
(1) N = 10*n + m, agree?
Now you tell me that the sum of the two digits is 1/7th of N or
(2) n + m = 1/7*(10*n + m)
You also tell me that the units digit is 3 or
(3) m = 3
Now to solve, put (3) into (2) and get
(4) n + 3 = 1/7*(10*n + 3) or
(5) 7*n + 21 = 10*n + 3, where I simply multiplied both sides by 7.
or
(6) 3*n = 18 or
(7) n = 6
Therefore your number is from (1)
(8) N = 10*6 + 3 or
(9) N = 63, voila! The wizard strikes again. lol

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