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?
+129840 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
