There are a total of 755 buffaloes, goats, geese and hens at a farm. The number of geese was 375 more than the number of buffaloes. The total number of goats and hens was 3 times the number of buffaloes.

1. How many goats and hens were there at the farm?
2. The total number of legs for all the goats and hens was 494. How many goats were there in the farm?

(a)
Number of buffaloes = 1 u
Number of goats and hens = 3 u
Number of geese = 1 u + 375

Total number of animals
= 1 u + 3 u + 1 u + 375
= 5 u + 375

5 u + 375 = 755
5 u = 755 - 375
5 u = 380

1 u = 380 ÷ 5 = 76

Number of goats and hens
= 3 u
= 3 x 76
= 228

(b)

Number of goats	Number of goats' legs	Number of hens	Number of hens' legs	Total
228	228 x 4 = 912	0	0	912
227	227 x 4 = 908	1	1 x 2 = 2	910
19	19 x 4 = 76	209	209 x 2= 418	494

Total number of goats and hens = 228

Total number of legs if all of them are goats
= 228 x 4 
= 912

Big difference in the total number of legs between the goats and the hens
= 912 - 494
= 418

Small difference in number of legs between one goat and one hen
= 4 - 2 
= 2

Number of hens
= 418 ÷ 2 
= 209

Number of goats
= 228 - 209
= 19

Answer(s): (a) 228; (b) 19