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sophie's favorite number is a two-digit number. if she reverses the digits, the result is $45$ less than her favorite number. the sum of the digits in her favorite number is $11$. what is sophie's favorite number?



Answer :

Sophie's favorite number is 83

We have that;

A two-digit number is Sophie's preferred number. Her favorite number is 45 less when the digits are in reverse. Her favorite number has digits that add out to 11 in total.

To get Sophie's favorite number, we need to assume the case as;

Let,

⇒10x + y = 10y + x + 45

   x + y = 11

   y = 11-x

⇒10x + 11 - x = 10(11 - x) + x + 45

  10x + 11 - x = 110 - 10x + x + 45

  9x + 11 = 155 - 9x

  18x + 11 = 155

  18x = 144

  x = 8

Therefore, y = 11 - 8

                  y = 3

Sum = x + y = 8 + 3 = 11

Hence, the given condition is satisfied.

Sophie's favorite number is 83.

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