There are a total of 717 sheep, donkeys, hens and ducks at a farm. The number of hens was 397 more than the number of sheep. The total number of donkeys and ducks was 2 times the number of sheep.
- How many donkeys and ducks were there at the farm?
- The total number of legs for all the donkeys and ducks was 632. How many donkeys were there in the farm?
(a)
Number of sheep = 1 u
Number of donkeys and ducks = 2 u
Number of hens = 1 u + 397
Total number of animals
= 1 u + 2 u + 1 u + 397
= 4 u + 397
4 u + 397 = 717
4 u = 717 - 397
4 u = 320
1 u = 320 ÷ 4 = 80
Number of donkeys and ducks
= 2 u
= 2 x 80
= 160
(b)
Number of donkeys |
Number of donkeys' legs |
Number of ducks |
Number of ducks' legs |
Total
|
160
|
160 x 4 = 640 |
0
|
0
|
640
|
159
|
159 x 4 = 636 |
1
|
1 x 2 = 2 |
638
|
156
|
156 x 4 = 624 |
4
|
4 x 2= 8 |
632
|
Total number of donkeys and ducks = 160
Total number of legs if all of them are donkeys
= 160 x 4
= 640
Big difference in the total number of legs between the donkeys and the ducks
= 640 - 632
= 8
Small difference in number of legs between one donkey and one duck
= 4 - 2
= 2
Number of ducks
= 8 ÷ 2
= 4
Number of donkeys
= 160 - 4
= 156
Answer(s): (a) 160; (b) 156