Question 269364: A number consist of two digit whose sum is 5. When the digits are reversed, tne number becomes greater by 9.Find the number:
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A number consist of two digit whose sum is 5. When the digits are reversed, tne number becomes greater by 9.Find the number:
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Let the number be 10t+u where t is the tens and u is the units digit.
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Equations:
t + u = 5
10u+t = 10t+u +9
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Simplify :
t + u = 5
9u - 9t = 9
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t + u = 5
-t+u = 9
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Add:
2u = 14
u = 7
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But, if u = 7, then t= -2
and that makes no sense
for a 2-digit number.
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Cheers,
Stan H.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! A number consist of two digit whose sum is 5. When the digits are reversed, tne number becomes greater by 9.Find the number:
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It has to be 14 or 23
It's 23
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The difference when you reverse digits is always a multiple of 9.
1*9
2*9
3*9
4*9 etc
The multiplier of 9 is the difference between the digits.
eg, for 37, the difference is 4, so 4*9 will be the change when the digits are reversed.
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For your problem, the multiplier of 9 is 1, so the difference between the digits is 1.
That makes the problem simpler:
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The sum of the digits is 5
The difference of the digits is 1
u + t = 5
u - t = 1
------------ Add
2u = 6
u = 3
t = 2
--> 23
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The long way:
10t + u = 10u + t - 9
t + u = 5
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9t - 9u = -9
t - u = -1
t + u = 5
2t = 4
t = 2
u = 3
--> 23
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