Answer:
The minimum of cows he needs are: 2
Step-by-step explanation:
There's a relation between each animal:
5 chickens equals 1 pig
3 pigs equals 2 sheep
5 sheep equals 2 cows
You can understand it as the following three abstractions:
5c = 1p (1)
3p = 2s (2)
5s = 2o (3)
Where:
c is for chickens
p is for pigs
s is for sheep
o is for cows
So now you have three equations with 4 variables. The next step is to obtain an equation that relates directly the variable c (chickens) with the variable o (cows). In order to do that from the equation 2 we obtain s in terms of p, as follow:
[tex]3p =2s\\s=\frac{3p}{2} \\[/tex]
Then we replace s in the equation 3 and we obtain v in terms of p:
[tex]5(\frac{3p}{2} )=2v\\\\2v=\frac{15}{2} p\\\\[/tex]
[tex]v=\frac{15}{2*2} p \\\\v=\frac{15}{4} p[/tex]
Now we replace v in the equation 1:
[tex]4c = \frac{4}{15} v[/tex]
[tex]c=\frac{1}{15} v[/tex] (4)
The equation 4 means that 1 chicken equals the fifteenth part of a cow. For this case the farmer needs 20 chikens, so we multiply per 20 each part of the equation 4:
[tex]20c = 20 * \frac{1}{15} v\\ \\\ 20c = \frac{20}{15}v = \frac{4}{3}v \\\\20c = 1.3333v[/tex]
As it is impossible to have 1.3333 cows, the answer is 2 cows approximately.
