Question 501679: if 18 is added to a two digit number, the digits are reversed. the sum of two digits is 8. what is the original number.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! if 18 is added to a two digit number, the digits are reversed. the sum of two digits is 8. what is the original number.
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If the digits are reversed, the one's place becomes the ten's place and vice versa.
Let t = the tens place digit
Let o = the ones place digit
If 18 is added, that means the tens place becomes t + 1 and the ones place becomes o + 8
However, if the sum o + 8 is greater than 9, then we need to carry a 1 to the tens place
The only way o + 8 < 10 is if o = 1. Since the sum of the digits is 8, that
would mean the tens digit would have to be 7. 71+18 does not equal 17, so we need to carry a 1.
So we can write this equation for the tens digit:
t + 2 = o
And since the sum of the digits is 8, we have:
t + o = 8
Substitute the value for o above into the last equation:
t + t + 2 = 8
2t = 6
t = 3
Therefore, o = 5
Ans: 35
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