There are a total of 786 donkeys, sheep, geese and chickens at a farm. The number of geese was 354 more than the number of donkeys. The total number of sheep and chickens was 2 times the number of donkeys.
- How many sheep and chickens were there at the farm?
- The total number of legs for all the sheep and chickens was 500. How many sheep were there in the farm?
(a)
Number of donkeys = 1 u
Number of sheep and chickens = 2 u
Number of geese = 1 u + 354
Total number of animals
= 1 u + 2 u + 1 u + 354
= 4 u + 354
4 u + 354 = 786
4 u = 786 - 354
4 u = 432
1 u = 432 ÷ 4 = 108
Number of sheep and chickens
= 2 u
= 2 x 108
= 216
(b)
Number of
sheep |
Number of
sheep' legs |
Number of
chickens |
Number of
chickens' legs |
Total
|
216
|
216 x 4 =
864 |
0
|
0
|
864
|
215
|
215 x 4 =
860 |
1
|
1 x 2 =
2 |
862
|
34
|
34 x 4 =
136 |
182
|
182 x 2=
364 |
500
|
Total number of sheep and chickens = 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 chickens
= 864 - 500
= 364
Small difference in number of legs between one sheep and one chicken
= 4 - 2
= 2
Number of chickens
= 364 ÷ 2
= 182
Number of sheep
= 216 - 182
= 34
Answer(s): (a) 216; (b) 34
