Complex Word problem?

Question

while walking by a farmyard filled with chickens and rabbits, a farmer decided to count the heads and feet of his animals. He came up with a sum of 100 (counting both heads and feet). How many of each animal were in the farmyard?

Answer 1

Without further information, there are a lot of possible correct answers.

Chickens each have 1 head and 2 feet (a total of 3 things being counted), and rabbits each have 1 head and 4 feet (5 things counted). This means the farmer is counting 3 for each chicken (3c) and 5 for each rabbit (5r).

3c + 5r = 100. Solving for r and adding -3c,
5r = 100 - 3c. Dividing by 5,
r = 20 - (3/5)c.

Now, the number of rabbits and the number of chickens must be a whole number. This means the number of chickens must be divisible by 5, or else you'd get a fraction for the number of rabbits. c has to be in the set of {0, 5, 10, 15, 20, 25, 30}. [If c > 33.333..., then r becomes less than 0, and you can't have a negative number of rabbits.]

If c = 0, then r = 20.
If c = 5, then r = 17.
If c = 10, then r = 14.
If c = 15, then r = 11.
If c = 20, then r = 8.
If c = 25, then r = 5.
If c = 30, then r = 2.

Answer 2

Sounds like insufficient information to give a specific answer.

Each rabbit has four feet and one head, so it counts for five toward the total; each chicken has two feet and one head, so it counts for three.

5r + 3c = 100

One possibility is 20 rabbits and no chickens. But you can take three rabbits away, and replace them with five chickens (17 rabbits and five chickens: 17*5 + 3*5 = 85 + 15 = 100), and so on all the way down to two rabbits and thirty chickens.

Answer 3

Let
number of heads and feet for chickens = 1 + 2 = 3
number of heads and feet for rabbits = 1 + 4 = 5

c = number of chickens
r = number of rabbits

Then we have the equation

3c + 5r = 100

Any solution where c and r are non-negative integers is valid.
c is a multiple of 5.

(c, r) = (0, 20), (5, 17), (10, 14), ... (30, 2).

Answer 4

wow! Im just gonna make a guess.......

hmm 150 feet and 25 heads devided by two or something.....
25 chickens and 75 rabbits?
I didn't really put much effort into this so if it is especially embarrasing dont blame my brain~