SOLUTION: The sum of the digits of a two-digit number is 10. If the digits are reversed,the new number is one less than twice the original number. What is the number?

Question 82511: The sum of the digits of a two-digit number is 10. If the digits are reversed,the new number is one less than twice the original number. What is 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 10. If the digits are reversed,the new number is one less than twice the original number. What is the number?
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Comment: Any two-digit number can be expressed as 10t+u where
t is the ten's digit and u is the unit's digit.
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EQUATION;
t+u = 10
10u+t = 2(10t+u)-1
Simplify the 2nd equation as follows:
10u+t = 20t+2u-1
19t-8u=1
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Rewrite as follows:
t+u=10
19t-8u=1
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t=10-u
Substitute into the 2nd equation to solve for u, as follows:
19(10-u)-8u=1
190-27u=1
27u=189
u=7
Then t=10-u=3
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The original number is 37
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Cheers,
Stan H.
:

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