Answer:
8
Step-by-step explanation:
The given ratios can be combined to a composite ratio using least common multiples.
<h3>Given ratios</h3>
We can identify each of the entities with a 2-letter designation:
TT - Tumtum tree; TW - tulgey wood; BS - frumious Bandersnatch;
ST - slithy tove; BG - borogoves; MR - mome raths; JW - Jabberwocky;
JB - Jubjub birds.
Then the given ratios are ...
- 20 TT : 1 TW
- 1 TW : 1 BS
- 5 ST : 2 BG
- 2 MR : 1 JW
- 2 JB : 200 TT . . . . (reduces to 1 : 100)
- 200 MR : 1 BG
- 5 JB : 1 ST
<h3>Composite ratios</h3>
The path from BS to JW is unique, so we can work our way there one ratio at a time. Having done this once, we can go back and do it again with the least possible multiplier.
Here, that turns out to be 125 Bandersnatches. We can combine these to the composite ratio ...
125 BS : 125 TW : 2500 TT : 25 JB : 5 ST : 2 BG : 400 MR : 200 JW
Then the ratio of Bandersnatches to Jabberwocks is 125 : 200 = 5 : 8.
If there are 5 frumious Bandersnatches, there should be 8 Jabberwocks.
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<em>Additional comment</em>
We know 1 JW : 2 MR and 200 MR : 1 BG. In order to get a common value of 200 MR in these ratios, we need to multiply the first by 100:
100 JW : 200 MR : 1 BG
Next, we notice the other ratio involving BG is 2 BG : 5 ST, which means we need to multiply by 2 again:
200 JW : 400 MR : 2 BG : 5 ST
The number of JB is 5 times the number of ST, so this extends to ...
... 5 ST : 25 JB
The number of TT is 100 times the number of JB, so we have ...
... 5 ST : 25 JB : 2500 TT
Continuing in like fashion, we get the composite ratio shown above. We originally worked this starting from BS. Reducing the JB/TT ratio from 2/200 to 1/100 helped eliminate an extra factor of 2.
