Goodness me - how complicated!
If the question is an exam one, then the calculations are correct.
That most of us wouldn't do it that way is a given. Those who are good at mental arithmetic while flying single pilot IFR will have no problems. Me, I get into brainfade, so I have a simple rule.
I climb at 500fpm (until the poor aeroplane says "enough"), and I descend at 500 fpm (unless there's a good reason that requires something else).
Conveniently, my Arrow flies close enough to 120 knots that 500 fpm allows me to use 4 miles per thousand feet as my standard. KISS is the only way for old lags like me.
Then, I learned the "numbers" that go with that. For example, if I'm cruising at 23/23, reducing MP to 17 inches will set me up neatly for 500fpm down. KISS again.