Question 280832: The sum of the digits of a two digit number is 14. If 36 is subtracted from the number, the resulting number is the original number with its digits interchangeable. Find the Number.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! When doing sum of digits problems, you have to remember that numbers like 'xy' are not being multiplied.
Consider the number 23.
It really is not "one" number, but instead it means 2*10 + 3*1.
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So the number is 'xy' but that is NOT x*y, it's just 'x' next to 'y'.
The value of the number 'xy' = 10x + y.
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x + y = 14 :: given
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36 is a value, so to subtract it, you have to calculate the value of xy:
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10x+y -36 = 10y + x
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Setting up a system of equations:
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10x + y - 36 - 10y - x = 0
9x - 9y = 36
x - y = 4
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x + y = 14
x - y = 4
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adding
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2x = 18
x = 9
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x + y = 14
given x = 9
y = 5
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so the original number, 'xy', appears to be 95.
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checking...
'yx' would be 59.
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so, is 95 - 36 = 59?
Yes, it is.
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Answer:
The number is 95.
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Done.
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