There are a total of 677 goats, sheep, chickens and geese at a farm. The number of chickens was 317 more than the number of goats. The total number of sheep and geese was 3 times the number of goats.
- How many sheep and geese were there at the farm?
- The total number of legs for all the sheep and geese was 476. How many sheep were there in the farm?
(a)
Number of goats = 1 u
Number of sheep and geese = 3 u
Number of chickens = 1 u + 317
Total number of animals
= 1 u + 3 u + 1 u + 317
= 5 u + 317
5 u + 317 = 677
5 u = 677 - 317
5 u = 360
1 u = 360 ÷ 5 = 72
Number of sheep and geese
= 3 u
= 3 x 72
= 216
(b)
Number of
sheep |
Number of
sheep' legs |
Number of
geese |
Number of
geese' legs |
Total
|
216
|
216 x 4 =
864 |
0
|
0
|
864
|
215
|
215 x 4 =
860 |
1
|
1 x 2 =
2 |
862
|
22
|
22 x 4 =
88 |
194
|
194 x 2=
388 |
476
|
Total number of sheep and geese = 216
Total number of legs if all of them are sheep
= 216 x 4
= 864
Big difference in the total number of legs between the sheep and the geese
= 864 - 476
= 388
Small difference in number of legs between one sheep and one goose
= 4 - 2
= 2
Number of geese
= 388 ÷ 2
= 194
Number of sheep
= 216 - 194
= 22
Answer(s): (a) 216; (b) 22
