Answer:
47
Step-by-step explanation:
Given 3 persons per horse, 4 sheep per cow, 3 ducks per person, you want to know if the total number of people, horses, sheep, cows, and ducks can be any of 41, 47, 59, 61, or 66.
Ratios
Using {d, p, h, s, c} for numbers of {ducks, people, horses, sheep, cows}, the given ratios are ...
- p : h = 3 : 1
- s : c = 4 : 1
- d : p = 3 : 1
We can combine the first and last of these to d : p : h = 9 : 3 : 1.
In terms of horses, the total number of horses, people, and ducks will be ...
h(1 + 3 + 9) = 13h
In terms of cows, the total number of sheep and cows will be ...
c(1 + 4) = 5c
Then the total Hamlet population will be (13h +5c).
Not possible
We need to find the number on the given list that cannot be expressed as this sort of sum.
In the attachment, we do that by subtracting multiples of 13 from the offered choice, and seeing if any remainders are divisible by 5. The cases where subtracting a multiple of 13 gives a multiple of 5 are highlighted.
Only 47 cannot be a total of people, horses, sheep, cows, and ducks.
