There are a total of 661 pigs, sheep, ducks and geese at a farm. The number of ducks was 306 more than the number of pigs. The total number of sheep and geese was 3 times the number of pigs.
- How many sheep and geese were there at the farm?
- The total number of legs for all the sheep and geese was 688. How many sheep were there in the farm?
(a)
Number of pigs = 1 u
Number of sheep and geese = 3 u
Number of ducks = 1 u + 306
Total number of animals
= 1 u + 3 u + 1 u + 306
= 5 u + 306
5 u + 306 = 661
5 u = 661 - 306
5 u = 355
1 u = 355 ÷ 5 = 71
Number of sheep and geese
= 3 u
= 3 x 71
= 213
(b)
Number of
sheep |
Number of
sheep' legs |
Number of
geese |
Number of
geese' legs |
Total
|
213
|
213 x 4 =
852 |
0
|
0
|
852
|
212
|
212 x 4 =
848 |
1
|
1 x 2 =
2 |
850
|
131
|
131 x 4 =
524 |
82
|
82 x 2=
164 |
688
|
Total number of sheep and geese = 213
Total number of legs if all of them are sheep
= 213 x 4
= 852
Big difference in the total number of legs between the sheep and the geese
= 852 - 688
= 164
Small difference in number of legs between one sheep and one goose
= 4 - 2
= 2
Number of geese
= 164 ÷ 2
= 82
Number of sheep
= 213 - 82
= 131
Answer(s): (a) 213; (b) 131
