There are a total of 750 sheep, pigs, chickens and ducks at a farm. The number of chickens was 342 more than the number of sheep. The total number of pigs and ducks was 2 times the number of sheep.

1. How many pigs and ducks were there at the farm?
2. The total number of legs for all the pigs and ducks was 664. How many pigs were there in the farm?

(a)
Number of sheep = 1 u
Number of pigs and ducks = 2 u
Number of chickens = 1 u + 342

Total number of animals
= 1 u + 2 u + 1 u + 342
= 4 u + 342

4 u + 342 = 750
4 u = 750 - 342
4 u = 408

1 u = 408 ÷ 4 = 102

Number of pigs and ducks
= 2 u
= 2 x 102
= 204

(b)

Number of pigs	Number of pigs' legs	Number of ducks	Number of ducks' legs	Total
204	204 x 4 = 816	0	0	816
203	203 x 4 = 812	1	1 x 2 = 2	814
128	128 x 4 = 512	76	76 x 2= 152	664

Total number of pigs and ducks = 204

Total number of legs if all of them are pigs
= 204 x 4 
= 816

Big difference in the total number of legs between the pigs and the ducks
= 816 - 664
= 152

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

Number of ducks
= 152 ÷ 2 
= 76

Number of pigs
= 204 - 76
= 128

Answer(s): (a) 204; (b) 128