Number Magic Algebraic Explanation

Pick a number from 1 to 9 (0<x<10). Multiply it by 2. Then add 3 to the result. Now multiply this number by 50, then add 1853 and subtract the year of you birth. You now should have a 3 digit number. The first digit is the number you picked above, and the last 2 digits are your age after your birthday this year (2003).
How is this possible? What is the algebraic explanation behind this?

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...t's write it as "1900+ 10a + b", subtracting this from what we obtained earlier:
100x+2003-(1900+10a+b)=100x-10a + 3-b (*)
the last expression is the decimal expression for a three digit number (because all of x, a and 3-b will be between 0 and 9): xa(3-b)
The first digit is ...