There are a total of 706 horses, pigs, hens and geese at a farm. The number of hens was 310 more than the number of horses. The total number of pigs and geese was 2 times the number of horses.
- How many pigs and geese were there at the farm?
- The total number of legs for all the pigs and geese was 424. How many pigs were there in the farm?
(a)
Number of horses = 1 u
Number of pigs and geese = 2 u
Number of hens = 1 u + 310
Total number of animals
= 1 u + 2 u + 1 u + 310
= 4 u + 310
4 u + 310 = 706
4 u = 706 - 310
4 u = 396
1 u = 396 ÷ 4 = 99
Number of pigs and geese
= 2 u
= 2 x 99
= 198
(b)
Number of
pigs |
Number of
pigs' legs |
Number of
geese |
Number of
geese' legs |
Total
|
198
|
198 x 4 =
792 |
0
|
0
|
792
|
197
|
197 x 4 =
788 |
1
|
1 x 2 =
2 |
790
|
14
|
14 x 4 =
56 |
184
|
184 x 2=
368 |
424
|
Total number of pigs and geese = 198
Total number of legs if all of them are pigs
= 198 x 4
= 792
Big difference in the total number of legs between the pigs and the geese
= 792 - 424
= 368
Small difference in number of legs between one pig and one goose
= 4 - 2
= 2
Number of geese
= 368 ÷ 2
= 184
Number of pigs
= 198 - 184
= 14
Answer(s): (a) 198; (b) 14
