Question 160558: the sum of the digits of a two-digit number is 11. If the digit is reversed, the new number increased by 20 is twice the original number. Find the original number.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! the sum of the digits of a two-digit number is 11. If the digit is reversed, the new number increased by 20 is twice the original number. Find the original number.
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Original number: 10t+u where t is the tens digit and u is the units digit.
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t + u = 11
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Digits reversed: 10u+t
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EQUATION:
10u+t+20 = 2(10t+u)
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Rearrange the equations:
t + u = 11
19t - 8u = 20
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Multiply thru 1st by 8 and add to solve for "t":
8t + 8u = 88
19t - 8u = 20
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27t = 108
t = 4 (the tens digit of the original number)
Since t+u = 11, u = 7 (the units digit of the original number)
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Original Number: 47
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Cheers,
Stan H.
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