SOLUTION: The sum of the digits of a two-digit number is 11. If 45 is added to the number, the result is the number with the digits reversed. find the number

Question 254359: The sum of the digits of a two-digit number is 11. If 45 is added to the number, the result is the number with the digits reversed. find the 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 45 is added to the number, the result is the number with the digits reversed. find the number
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Let the number be 10t+u where "t" is the tens digit and "u" is the units.
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Equations:
t + u = 11
10t+u+45 = 10u+t
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Rearrange the equations:
t + u = 11
9t-9u = -45
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Modify to get:
t + u = 11
t - u = 5
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Add and solve for "t":
2t = 16
t = 8 (the tens digit of the original number)
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Since t+u = 11, u = 3 (the units digit)
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Solution: The number is 83
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Cheers,
Stan H.
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