SOLUTION: Sum of the digits of a two digit number is 9. When We interchange the digits it is found that the resulting new number is greater than the original number by 27. WHAT is the two di

Algebra ->  Test -> SOLUTION: Sum of the digits of a two digit number is 9. When We interchange the digits it is found that the resulting new number is greater than the original number by 27. WHAT is the two di      Log On


   

Question 695133: Sum of the digits of a two digit number is 9. When We interchange the digits it is found that the resulting new number is greater than the original number by 27. WHAT is the two digit number?
Answer by stanbon(75887) About Me  (Show Source):
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Sum of the digits of a two digit number is 9. When We interchange the digits it is found that the resulting new number is greater than the original number by 27. WHAT is the two digit number?
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Let the original number be 10t+u
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Interchanged number is 10u+t
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Equations:
t + u = 9
10t+u - (10u+t) = 27
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Substitute for "t" using t = 9-u
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10(9-u)+u -10u-(9-u) = 27
90 - 10u + u -10u-9+u = 27
-18u + 81 = 27
-18u = -54
u = 3 (the unit's digit)
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Solve for "t" using t = 9-u
t = 9-3 = 6 (the ten's digit)
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Original Number: 10t+u = 63
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Cheers,
Stan H.
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