# Another Problem

1. Feb 2, 2004

### vepore2

Let us consider a two digit number. If the digits are interchanged, the new number is 9 more than the original number. The second digit of the original number is one more than the first digit. Find the number.
Let x be the first digit and y be the second digit

(10y + x) - (10x +y) = 9
and
y -x =1

(10y + x) - (10x +y) = 9
9y -9x = 9
y - x = 1

I find out that both equations are the same does that mean that there isn't enough information or have I done something wrong?
From messing around I find the number is 12

2. Feb 2, 2004

### Moose352

It is underdetermined. Any number where y-x = 1 will work.

3. Feb 3, 2004

### himanshu121

U can't find two seperate value OR unique Values

Generally the digits will be x at units place and 1+x at ten's digit and 0<x<9

4. Feb 3, 2004

### HallsofIvy

Staff Emeritus
What do you mean "From messing around I find the number is 12"? Just how messy were you? Did you think about 23? 34? 45? 56? 67? 89? All those number have exactly the properties you require. (Of course, that is exactly what Moose352 said: "Any number where y-x = 1 will work."