Question 277285: The sum of the digits of a two- digit number is 14. When the digits are reversed, the new number is 36 more than the original number. What is the original number?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! When solving number problems like these, we have to keep in mind the place values.
For example, the number 23 actually means 2*10 + 3*1.
Since the numbers are unknown in this word problem, we can call them 'xy'.
BUT keep in mind that they are just standing next to each other, they're not being multiplied.
The value would be 10x + y.
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We are told some characteristics of the number 'xy'...
x + y = 14
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That's easy, but the second statement is harder to set up.
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Remember, the VALUE of 'xy' is 10x + y.
So, reversing the digits to be 'yx' would change the VALUE to 10y + x.
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We're told
10y + x is 36 more than 10x + y, which algebraically is
10y+x = 10x+y+36
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Rearranging this equation we have:
x + 10y = 10x + y + 36
x -10x + 10y - y = 36
-9x + 9y = 36
dividing by 9
-x + y = 4
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Now we have to the two equations
x + y = 14
-x + y = 4
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Adding we obtain
2y = 18
y = 9
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Since x+y = 14, then x = 14-9 = 5
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Checking...
xy = 59
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yx = 95
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Is 95 = 59 + 36??
Yes.
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Answer:
The original number was 59.
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Done
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