Combined Weight

Let $L,S,G$ be the respective weights of the Lion, Salamander and Gerbil. Then we are given that

$L + S = 108, L + G = 104$ and $G + S = 8$ . Adding these equations together, we find that

$(L + S) + (L + G) + (G + S) = 108 + 104 + 8 \Longrightarrow 2L + 2S + 2G = 220 \Longrightarrow$

$2(L + S + G) = 220 \Longrightarrow L + S + G = \boxed{110}$ pounds.

Edit: As Calvin Lin notes in his comment, to be complete we should check that $L,S,G$ are all positive in this scenario. First note that

$(L + S) - (L + G) = 108 - 104 \Longrightarrow S - G = 4 \Longrightarrow$

$(S - G) + (G + S) = 4 + 8 \Longrightarrow 2S = 12 \Longrightarrow S = 6, G = S - 4 = 2, L = 108 - S = 102$ .

So the unique solution is $(L,S,G) = (102, 6, 2)$ , giving us $L + S + G = 110$ pounds as found above.

The easiest way to figure this out is to look at #3 first. If the gerbil and salamander weigh 8 pounds, then you can do 2 and 6. If the salamander weighs 6, then the lion weighs 102. If the gerbil weighs 2, then the lion weighs 102. So now we have

lion:102

Gerbil:2

Salamander:6

And, of course, if you add these up, you get 110!

L+S=108

L+G=104

SO,2L+S+G=`108+104=212

OR,2L+8=212 [Gerbil and salamander: 8 pounds]

OR,L=204/2=102

So, L+G+S=102+8=110