SOLUTION: The sum of the digits of two- digit numbers is 10. if the digits are reversed, the new number is 54 less than the original number. Find the original number.

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Question 103837: The sum of the digits of two- digit numbers is 10. if the digits are reversed, the new number is 54 less than the original number. Find the original number.
Found 2 solutions by stanbon, checkley75:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The sum of the digits of two- digit numbers is 10. if the digits are reversed, the new number is 54 less than the original number. Find the original number.
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Every two digit number can be written as 10t+u where t is the ten's digit
and u is the unit's digit.
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Your Problem:
EQUATIONS:
t+u = 10
10u+t= 10t+u-54
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Rearrange:
t+u=10
9t-9u=54
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Simplify:
1st; t+u=10
2nd: t-u=6
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Add 1st and 2nd and solve for t,as follows:
2t = 16
t = 8
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Substitute in t+u=10 to solve for u:
8+u=10
u = 2
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Original Number = 82
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Cheers,
Stan H.

Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
X+Y=10 OR X=10-Y
10X+Y=10Y+X-54 NOW REPLACE X IN THIS EQUATION BY (10-Y)
10(10-Y)+Y=10Y+(10-Y)+54
100-10Y+Y=10Y+10-Y+54
100-9Y=9Y+64
-18Y=-36
Y=-36/-18
Y=2 ANSWER FOR THE UNITS DIGIT.
X=10-2
X=8 ANSWER FOR THE TENS DIGIT.
PROOF
82=28+54
82=82