SOLUTION: can you please help me solve this problem and show all work using the 5-step method: (((When the digits of the two digit number are reversed, the new number is 9 more than the orig

Question 154659This question is from textbook Algebra structure and method book 1
: can you please help me solve this problem and show all work using the 5-step method: (((When the digits of the two digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?)) This question is from textbook Algebra structure and method book 1

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
When the digits of the two digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?
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Let the original number be 10t+u where t is the tens unit and u is the units digit.
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If you reverse the digits you get 10u+t
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EQUATION:
10u+t - (10t+u) = 9
t + u = 11
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Rearrange:
-9t + 9u = 9
t + u = 11
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Modify:
t -u = -1
t+u = 11
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Add to solve for t
2t = 10
t = 5
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since t+u = 11, u = 6
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The original number is 56
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Cheers,
Stan H.
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