<PRE><B>Question 68859</B>
The value of a certain 2 digit number is 5 times the sum of its digits. If the digits are reversed,the resulting number 9 more than the original number . Find the original number. T is supposed to represent the tens, and U is supposed to represent the unit.
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Value = 10T+U   (Just like 32 = 10(3)+2)
5 times sum of its digits = 5(T+U)
If digits are reversed Value = 10U+T
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EQUATIONS:
1st: 10T+U=5(T+U)
2nd: 10U+T = 10T+U+9
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Rewrite the equations:
1st becomes: 5T-4U=0
2nd becomes: 9T-9U+9=0
2nd again: T-U=-1
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Rewriting the two equations:
1st: 5T-4U=0
2nd:T-U=-1
Solve 2nd for T to get:
3rd: T=U-1
Substitute into 1st to get:
5(U-1)-4U=0
U=1
Substitute that into 3rd to get:
T=1-1=0
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The two digit number is 01
When you reverse it you get 10 which is 9 more than the original.
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Cheers,
Stan H.



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