SOLUTION: Sophie's favorite (positive) number is a two-digit number. If she reverses the digits, the result is 72 less than her favorite number. Also, one digit is 1 less than double the oth

Question 1208628: Sophie's favorite (positive) number is a two-digit number. If she reverses the digits, the result is 72 less than her favorite number. Also, one digit is 1 less than double the other digit. What is Sophie's favorite number?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The problem is faulty. There is no 2-digit number that satisfies both conditions.

For any 2-digit number, the difference between that number and the number with the digits reversed is always 9 times the difference between the two digits. Formally....

Let the 2-digit number be "AB"

The value of the 2-digit number is 10A+B; the value of the number with the digits reversed is 10B-A. The difference between the two numbers is

(10A+B)-(10B+A) = 9A-9B = 9(A-B)

In this problem, with a difference of 72 between the two 2-digit numbers, the difference between the two digits is 72/9 = 8. That means the two digits must be 1 and 9, making Sophie's favorite number 91. But that number doesn't satisfy the other given condition.

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