SOLUTION: The sum of the digits of a two digits number is 11.if the digits are interchanged. The number they form decreases by 9.find the number

Question 1121078: The sum of the digits of a two digits number is 11.if the digits are interchanged. The number they form decreases by 9.find the number
Found 3 solutions by Alan3354, solver91311, greenestamps:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
65
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Reversing a 2 digit number changes the number by 9 times the difference between the digits.

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Solve the 2X2 system for x and y

John

My calculator said it, I believe it, that settles it

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

You might want to play around with this a bit to see that it works, since problems like this involving reversing the digits of a 2-digit numbers are common.

You might even want to look at an algebraic proof that the method works....

When the digits of a 2-digit number are reversed, the difference between the original number and the new number is 9 times the difference between the two digits.

In this problem, the sum of the digits is 11; and when the digits are reversed the value of the number decreases by 9. Since 9 is 9*1, the difference between the two digits is 1.

So the two digits have to be 5 and 6; then, since the number decreases when the digits are reversed, the original number was 65.
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