Digital BW, The Print

Here's an example that might help:

I have a machine that collects money.  It provides one total for all coins,
and one total for all bills.  I have another machine that also collects
money, but it collects only quarters and five-dollar bills.

Using the first machine, I collect all the money I see around the house.
The totals displayed by the machine are $8.25 and $21.  Based on these
totals, I want to figure out what totals the second machine would have
given, had I used it to collect the money.  Can you explain how I would do
this?

The money around the house represents the spectral distribution of light in
an original scene.  The first machine represents color film; the second
machine represents B&W film.  Do you see the problem now?