Question

In reply to an inquiry about the animals on his farm, the farmer says: “I only ever keep sheep, goats, and horses. In fact, at the moment they are all sheep bar three, all goats bar four, and all horses bar five.” How many does he have of each animal?​

Answer 1

[tex][/tex] In reply to an inquiry about the animals on his farm, the farmer says: “I only ever keep sheep, goats, and horses. In fact, at the moment they are all sheep bar three, all goats bar four, and all horses bar five.” How many does he have of each animal?

X : the no. of sheep he owns

Y : the no. of goats he owns

Z : the no. of horses he owns

X + Y + Z = Total no. of animals he owns

He says that “They are all sheep bar three.” Which means, the no. of animals other than sheep is 3, i.e.

Y + Z = 3

Similarly,

X + Z = 4 and X + Y = 5

On adding all the three equations, we get

2 ( X + Y + Z ) = 12

This implies,

X + Y + Z = 6

This means that the farmers has a total of 6 animals. And on further solving the equations we find that the he has 3 sheep, 2 goats and a horse.

Answer 2

Answer:

Algebraically, we can represent this in two equations:

c + s = 32 (since each animal only has 1 head).

2c + 4s = 90 (chickens have 2 legs, and sheep have 4 legs - Assumption is that there are no odd-legged animals running around, such as a 3-legged sheep)

So, let’s express the first equation in terms of c by subtracting s from each side.

c = 32 - s

And we can substitute that into the second equation to get a single element that we are solving for.

2(32-s) + 4s = 90 (substitute the first equation into the second)

64 - 2s + 4s = 90 (get rid of parenthesis)

2s + 64 = 90

2s = 26

s = 13

Now, we have the number of sheep that there are. We’ve just got to substitute that into the first equation to get our number of chickens.

c = 32 - s

c = 32 - 13

c = 19

So, the answer is 19 chickens, and 13 sheep.