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?
The farmer has 3 sheep, 2 goats and 1 horse.
Using S, G and H for the number of sheep, goats and horses respectively, we can come up with the following equations:
S + G + H = total
G + H = 3
S + H = 4
S + G = 5
Adding the last 3 equations, we get:
2(S + G + H) = 12
S + G + H = 6
The farmer has a total of 6 animals. And on further solving the equations we find that the he has 3 sheep, 2 goats and 1 horse.