SOLUTION: 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 $6$.

Question 1209008: 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 $6$. What is Sophie's favorite number?

Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

For the original number we have
t = tens digit
u = units digit
That constructs 10t+u

For instance if the number is 23 then t = 2 and u = 3.
10t+u = 10*2+3 = 23.

The digits of Sophie's mystery number add to 6.
t+u = 6 which solves to u = 6-t
This will be useful in a substitution later.

10u+t is the result of reversing the digits. This is 45 less than her favorite number.

swapped = original - 45
10u + t = 10t+u - 45
10(u) + t = 10t+u - 45
10(6-t) + t = 10t+6-t - 45
60-10t+t = 10t+6-t-45
60-9t = 9t-39
-9t-9t = -39-60
-18t = -99
t = -99/(-18)
t = 5.5
We do not get a whole number result for the tens digit, so there must be a typo somewhere in your question.
Perhaps the digits add to something else other than 6?
Or maybe the "45" should be another value?
I would ask your teacher for clarification.

Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
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 $6$. What is Sophie's favorite number?
~~~~~~~~~~~~~~~~~~~~~~~~~

The given info that the difference of the number and the reversed number is 45
tells us that the difference of the digits is 45/9 = 5.

Hence, the digits are of different parity.

Then the sum of the digits can not be 6.   Contradiction.

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