There are a total of 687 donkeys, donkeys, hens and geese at a farm. The number of hens was 337 more than the number of donkeys. The total number of donkeys and geese was 3 times the number of donkeys.

1. How many donkeys and geese were there at the farm?
2. The total number of legs for all the donkeys and geese was 526. How many donkeys were there in the farm?

(a)
Number of donkeys = 1 u
Number of donkeys and geese = 3 u
Number of hens = 1 u + 337

Total number of animals
= 1 u + 3 u + 1 u + 337
= 5 u + 337

5 u + 337 = 687
5 u = 687 - 337
5 u = 350

1 u = 350 ÷ 5 = 70

Number of donkeys and geese
= 3 u
= 3 x 70
= 210

(b)

Number of donkeys	Number of donkeys' legs	Number of geese	Number of geese' legs	Total
210	210 x 4 = 840	0	0	840
209	209 x 4 = 836	1	1 x 2 = 2	838
53	53 x 4 = 212	157	157 x 2= 314	526

Total number of donkeys and geese = 210

Total number of legs if all of them are donkeys
= 210 x 4 
= 840

Big difference in the total number of legs between the donkeys and the geese
= 840 - 526
= 314

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

Number of geese
= 314 ÷ 2 
= 157

Number of donkeys
= 210 - 157
= 53

Answer(s): (a) 210; (b) 53