There are a total of 763 pigs, donkeys, hens and ducks at a farm. The number of hens was 375 more than the number of pigs. The total number of donkeys and ducks was 2 times the number of pigs.

1. How many donkeys and ducks were there at the farm?
2. The total number of legs for all the donkeys and ducks was 524. How many donkeys were there in the farm?

(a)
Number of pigs = 1 u
Number of donkeys and ducks = 2 u
Number of hens = 1 u + 375

Total number of animals
= 1 u + 2 u + 1 u + 375
= 4 u + 375

4 u + 375 = 763
4 u = 763 - 375
4 u = 388

1 u = 388 ÷ 4 = 97

Number of donkeys and ducks
= 2 u
= 2 x 97
= 194

(b)

Number of donkeys	Number of donkeys' legs	Number of ducks	Number of ducks' legs	Total
194	194 x 4 = 776	0	0	776
193	193 x 4 = 772	1	1 x 2 = 2	774
68	68 x 4 = 272	126	126 x 2= 252	524

Total number of donkeys and ducks = 194

Total number of legs if all of them are donkeys
= 194 x 4 
= 776

Big difference in the total number of legs between the donkeys and the ducks
= 776 - 524
= 252

Small difference in number of legs between one donkey and one duck
= 4 - 2 
= 2

Number of ducks
= 252 ÷ 2 
= 126

Number of donkeys
= 194 - 126
= 68

Answer(s): (a) 194; (b) 68