Question 280832
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.