There are a total of 673 sheep, donkeys, chickens and ducks at a farm. The number of chickens was 301 more than the number of sheep. The total number of donkeys and ducks was 2 times the number of sheep.

1. How many donkeys and ducks were there at the farm?
2. The total number of legs for all the donkeys and ducks was 568. How many donkeys were there in the farm?

(a)
Number of sheep = 1 u
Number of donkeys and ducks = 2 u
Number of chickens = 1 u + 301

Total number of animals
= 1 u + 2 u + 1 u + 301
= 4 u + 301

4 u + 301 = 673
4 u = 673 - 301
4 u = 372

1 u = 372 ÷ 4 = 93

Number of donkeys and ducks
= 2 u
= 2 x 93
= 186

(b)

Number of donkeys	Number of donkeys' legs	Number of ducks	Number of ducks' legs	Total
186	186 x 4 = 744	0	0	744
185	185 x 4 = 740	1	1 x 2 = 2	742
98	98 x 4 = 392	88	88 x 2= 176	568

Total number of donkeys and ducks = 186

Total number of legs if all of them are donkeys
= 186 x 4 
= 744

Big difference in the total number of legs between the donkeys and the ducks
= 744 - 568
= 176

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

Number of ducks
= 176 ÷ 2 
= 88

Number of donkeys
= 186 - 88
= 98

Answer(s): (a) 186; (b) 98