There are a total of 629 cows, pigs, ducks and hens at a farm. The number of ducks was 379 more than the number of cows. The total number of pigs and hens was 3 times the number of cows.
- How many pigs and hens were there at the farm?
- The total number of legs for all the pigs and hens was 444. How many pigs were there in the farm?
(a)
Number of cows = 1 u
Number of pigs and hens = 3 u
Number of ducks = 1 u + 379
Total number of animals
= 1 u + 3 u + 1 u + 379
= 5 u + 379
5 u + 379 = 629
5 u = 629 - 379
5 u = 250
1 u = 250 ÷ 5 = 50
Number of pigs and hens
= 3 u
= 3 x 50
= 150
(b)
Number of
pigs |
Number of
pigs' legs |
Number of
hens |
Number of
hens' legs |
Total
|
150
|
150 x 4 =
600 |
0
|
0
|
600
|
149
|
149 x 4 =
596 |
1
|
1 x 2 =
2 |
598
|
72
|
72 x 4 =
288 |
78
|
78 x 2=
156 |
444
|
Total number of pigs and hens = 150
Total number of legs if all of them are pigs
= 150 x 4
= 600
Big difference in the total number of legs between the pigs and the hens
= 600 - 444
= 156
Small difference in number of legs between one pig and one hen
= 4 - 2
= 2
Number of hens
= 156 ÷ 2
= 78
Number of pigs
= 150 - 78
= 72
Answer(s): (a) 150; (b) 72
