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Workings

Hints
The first letters of the words are: M, C, C, S, V, G, A, T, S, T, S, F, S, D, O.

Answers
---rix = matrix ---osy = choosy ---few = curfew ---oze = snooze ---uum = vacuum ---wth = growth ---nda = agenda ---nis = tennis ---tem = system ---pod = tripod ---reo = stereo ---hom = fathom ---gan = slogan ---amt = dreamt ---gen = oxygen

Workings

Hint
The answer is not 15.

Answer
19 bottles.

Reasoning
From the initial 77 bottles, 75 bottles can be recycled for 15 new full bottles.

Once those are drunk, Alex will have 17 empty bottles (15 plus the 2 extra empty bottles).

From the 17 empty bottles, 15 bottles can be recycled for 3 new full bottles.

Once those are drunk, Alex will have 5 empty bottles (3 plus the 2 extra empty bottles), which can be recycled for one final full bottle.

Giving a total of 15 + 3 + 1 = 19.

Workings

Hint
How many rooms can Alex clear in 36 hours?

Answer
12 hours.

Reasoning
In 36 hours, Alex could empty 2 lots of bookshelves, Billie could also empty 2 lots of bookshelves, and Drew could refill 1 lot of bookshelves.

So, 2 + 2 − 1 = 3 lots of bookshelves in 36 hours. Which is 12 hours for one lot of bookshelves.

Alternative Reasoning
Alex and Billie can each empty ¹/₁₈ of the bookshelves in 1 hour, but Drew will refill ¹/₃₆ of the bookshelves in one hour.

So in one hour we have ¹/₁₈ + ¹/₁₈ − ¹/₃₆ = ¹/₁₂.

So it would take 12 hours to empty the bookshelves.

Workings

Hint
The next-to-last letters are: N, N, E, I, L, O, R, E, U, U.

Answers
-s-e-d = ascend -p-a-g = sprang -r-f-r = prefer -y-r-d = hybrid -r-f-e = trifle -a-b-n = carbon -a-e-a = camera -m-z-s = amazes -s-f-l = useful -i-s-e = tissue