SOLUTION: If 18 is added to a two-digit number, the digits are reversed. The sum of the digits = 8. What is the original number?

Question 530303: If 18 is added to a two-digit number, the digits are reversed. The sum of the digits = 8. What is the original number?

Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
The easiest way to solve this is to think logically about the givens provided. They narrow the potential solution set way down to a handful of possible answers. Then picking the right answer becomes very obvious.
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The best clue is: the sum of the digits = 8. Think of all the 2-digit numbers as an ordered pair of single digits. For example, let's set:
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d1 = 1st digit,
d2 = 2nd digit
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That is, instead of thinking of the number as d1d2, think of it as d1, d2. Then, going back to d1 + d2 = 8, the possible 2-digit numbers are:
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08 (0, 8)
17 (1, 7)
26 (2, 6)
35 (3, 5)
44 (4, 4)
53 (5, 3)
62 (6, 2)
71 (7, 1)
80 (8, 0)
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The next condition was adding 18 to the number reverses the digits. So, add 18 to all of the numbers above:
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08 + 18 = 26
17 + 18 = 35
26 + 18 = 44
35 + 18 = 53 (which gives us the reversed digits)
44 + 18 = 62
53 + 18 = 71
62 + 18 = 80
71 + 18 = 89
80 + 18 = 98
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Hence, our original number is 35
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cheers,
Lee
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PS. This could be easily solved with linear equations; however, not as quickly as this method, in this instance. I can show you the other method if you like... 8-)
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