Five digits and one

Here is a nice place value puzzle I saw on the Maths is Fun website.

Puzzle

I am thinking of a five digit number. If you were to put a "1" at the end of the number you would get a six digit number which is three times the six digit number you get by placing a "1" at the front of my number. What number am I thinking of?

Help

Hint

An algebraic solution exists: let $x$ be the mystery number. How do you express the two six digit numbers in terms of $x$?

References

Maths is Fun - math and logic puzzles appropriate for math education.