There are a total of 749 sheep, pigs, chickens and hens at a farm. The number of chickens was 337 more than the number of sheep. The total number of pigs and hens was 2 times the number of sheep.
- How many pigs and hens were there at the farm?
- The total number of legs for all the pigs and hens was 606. How many pigs were there in the farm?
(a)
Number of sheep = 1 u
Number of pigs and hens = 2 u
Number of chickens = 1 u + 337
Total number of animals
= 1 u + 2 u + 1 u + 337
= 4 u + 337
4 u + 337 = 749
4 u = 749 - 337
4 u = 412
1 u = 412 ÷ 4 = 103
Number of pigs and hens
= 2 u
= 2 x 103
= 206
(b)
Number of
pigs |
Number of
pigs' legs |
Number of
hens |
Number of
hens' legs |
Total
|
206
|
206 x 4 =
824 |
0
|
0
|
824
|
205
|
205 x 4 =
820 |
1
|
1 x 2 =
2 |
822
|
97
|
97 x 4 =
388 |
109
|
109 x 2=
218 |
606
|
Total number of pigs and hens = 206
Total number of legs if all of them are pigs
= 206 x 4
= 824
Big difference in the total number of legs between the pigs and the hens
= 824 - 606
= 218
Small difference in number of legs between one pig and one hen
= 4 - 2
= 2
Number of hens
= 218 ÷ 2
= 109
Number of pigs
= 206 - 109
= 97
Answer(s): (a) 206; (b) 97
