There are a total of 701 goats, donkeys, ducks and hens at a farm. The number of ducks was 365 more than the number of goats. The total number of donkeys and hens was 2 times the number of goats.

1. How many donkeys and hens were there at the farm?
2. The total number of legs for all the donkeys and hens was 620. How many donkeys were there in the farm?

(a)
Number of goats = 1 u
Number of donkeys and hens = 2 u
Number of ducks = 1 u + 365

Total number of animals
= 1 u + 2 u + 1 u + 365
= 4 u + 365

4 u + 365 = 701
4 u = 701 - 365
4 u = 336

1 u = 336 ÷ 4 = 84

Number of donkeys and hens
= 2 u
= 2 x 84
= 168

(b)

Number of donkeys	Number of donkeys' legs	Number of hens	Number of hens' legs	Total
168	168 x 4 = 672	0	0	672
167	167 x 4 = 668	1	1 x 2 = 2	670
142	142 x 4 = 568	26	26 x 2= 52	620

Total number of donkeys and hens = 168

Total number of legs if all of them are donkeys
= 168 x 4 
= 672

Big difference in the total number of legs between the donkeys and the hens
= 672 - 620
= 52

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

Number of hens
= 52 ÷ 2 
= 26

Number of donkeys
= 168 - 26
= 142

Answer(s): (a) 168; (b) 142