Mental-jaunt #2 (February 4, 2014)

In a very old book on my shelf it says:

Pick any three digits from 1 through 9 and write them down as a three-digit number. Let's call them a, b and c. For example if I chose 538, then a=5, b=3 and c=8. Now run through the following chain on your calculator:

a X 2 + 3 X 5 + b X 10 + c - 150

The answer will be the three digit number you wrote down.

a) Try this out. I did, and it did not work for me, did it work for you?

b) If not, assuming there is a typographical error or two, can you correct this?

c) If not, assuming there is no typographical error, what is going on?

d) Share the mental-jaunt you went on with someone - explaining what you were thinking at the very start and how you reached your destination.