There are a total of 682 cows, sheep, geese and hens at a farm. The number of geese was 367 more than the number of cows. The total number of sheep and hens was 3 times the number of cows.
- How many sheep and hens were there at the farm?
- The total number of legs for all the sheep and hens was 544. How many sheep were there in the farm?
(a)
Number of cows = 1 u
Number of sheep and hens = 3 u
Number of geese = 1 u + 367
Total number of animals
= 1 u + 3 u + 1 u + 367
= 5 u + 367
5 u + 367 = 682
5 u = 682 - 367
5 u = 315
1 u = 315 ÷ 5 = 63
Number of sheep and hens
= 3 u
= 3 x 63
= 189
(b)
Number of
sheep |
Number of
sheep' legs |
Number of
hens |
Number of
hens' legs |
Total
|
189
|
189 x 4 =
756 |
0
|
0
|
756
|
188
|
188 x 4 =
752 |
1
|
1 x 2 =
2 |
754
|
83
|
83 x 4 =
332 |
106
|
106 x 2=
212 |
544
|
Total number of sheep and hens = 189
Total number of legs if all of them are sheep
= 189 x 4
= 756
Big difference in the total number of legs between the sheep and the hens
= 756 - 544
= 212
Small difference in number of legs between one sheep and one hen
= 4 - 2
= 2
Number of hens
= 212 ÷ 2
= 106
Number of sheep
= 189 - 106
= 83
Answer(s): (a) 189; (b) 83
