How to inexpensively eliminate airplane noise when listening to programming on an airline flight

A recent product review at on The Globe and Mail website touted a noise-cancelling headphone by Phitek (an offering not unique to Phitek). A suggested use of the headphone was to cancel noise while listening to programming on an airline flight. There is, however, an inexpensive way to eliminate noise that doesn't involve buying expensive headphones.

Here is how to solve the airplane noise problem for about $0.25. I've travelled millions of long-haul miles as a service engineer and this is what worked for me.
Buy some foam ear plugs at the pharmacy. The ones connected by a plastic tether are most convenient. Wear the ear plugs and put the airline's cheap earphones over top. Then crank the volume. The aircraft noise will be attenuated, whereas the program volume will be as desired. Here's the math: let N be the airplane noise volume, P be the normal program volume if you were listening with no noise and A be the attenuation of the ear plugs (A is a small positive number less that 1). When you crank the volume so that you can hear it at the desired volume, what you are doing is increasing the volume by a factor of 1/A (1/A is a large positive number) over what you would normally have it at. With this setup you will hear the program as A[(1/A)P + N] = P + AN. Since A is very small, AN is much smaller that the airplane noise, N.
So, you get the normal program volume with airline noise greatly attenuated. The program sound fidelity is very good and there is no hissing as from the noise cancelling headphones. You can actually enjoy a movie now!