SOLUTION: The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more than the original number. Find the number.

Algebra ->  Systems-of-equations -> SOLUTION: The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more than the original number. Find the number.      Log On


   

Question 120012: The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more than the original number. Find the number.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more than the original number. Find the number.
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Let the two-digit number be 10t+u where t is the tens digit and u the units digit.
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EQUATION:
t+u = 11
10u+t = 10t+u + 45
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Rearrange the equations:
t+u = 11
9t-9u = -45
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Simplify:
t+u = 11
t-u = -5
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Add the equations to solve for "t":
2t = 6
t = 3
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Substitute to solve for "u":
3+u = 11
u = 8
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The original number is 38
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Cheers,
Stan H.