Sophie's favorite number is a two-digit number. If she reverses the digits, the result is 36 less than her favorite number. Also, one digit is 1 less than double the other digit. What is Sophie's favorite number?

Guest Aug 5, 2023

#1**+1 **

Let the smaller digit = d

Let the larger digit = 2d - 1

So the larger number can be expressed as 10(2d-1) + d

And the smaller number can be expressed as 10d + 2d -1

And the difference between these = 36 .....so......

[10(2d -1) + d] - [ 10d + 2d -1] = 36 simplify

20d -10 + d - 10d -2d + 1 = 36

9d - 9 = 36

9d = 36 + 9

9d =45

d = 45/9 = 5

2d -1 = 9

Her favorite number = 95 and the other is 59 and their difference = 36

CPhill Aug 5, 2023