There are a total of 794 goats, horses, geese and chickens at a farm. The number of geese was 339 more than the number of goats. The total number of horses and chickens was 3 times the number of goats.

1. How many horses and chickens were there at the farm?
2. The total number of legs for all the horses and chickens was 628. How many horses were there in the farm?

(a)
Number of goats = 1 u
Number of horses and chickens = 3 u
Number of geese = 1 u + 339

Total number of animals
= 1 u + 3 u + 1 u + 339
= 5 u + 339

5 u + 339 = 794
5 u = 794 - 339
5 u = 455

1 u = 455 ÷ 5 = 91

Number of horses and chickens
= 3 u
= 3 x 91
= 273

(b)

Number of horses	Number of horses' legs	Number of chickens	Number of chickens' legs	Total
273	273 x 4 = 1092	0	0	1092
272	272 x 4 = 1088	1	1 x 2 = 2	1090
41	41 x 4 = 164	232	232 x 2= 464	628

Total number of horses and chickens = 273

Total number of legs if all of them are horses
= 273 x 4 
= 1092

Big difference in the total number of legs between the horses and the chickens
= 1092 - 628
= 464

Small difference in number of legs between one horse and one chicken
= 4 - 2 
= 2

Number of chickens
= 464 ÷ 2 
= 232

Number of horses
= 273 - 232
= 41

Answer(s): (a) 273; (b) 41