There are a total of 663 horses, cows, hens and ducks at a farm. The number of hens was 339 more than the number of horses. The total number of cows and ducks was 4 times the number of horses.
- How many cows and ducks were there at the farm?
- The total number of legs for all the cows and ducks was 576. How many cows were there in the farm?
(a)
Number of horses = 1 u
Number of cows and ducks = 4 u
Number of hens = 1 u + 339
Total number of animals
= 1 u + 4 u + 1 u + 339
= 6 u + 339
6 u + 339 = 663
6 u = 663 - 339
6 u = 324
1 u = 324 ÷ 6 = 54
Number of cows and ducks
= 4 u
= 4 x 54
= 216
(b)
Number of
cows |
Number of
cows' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
216
|
216 x 4 =
864 |
0
|
0
|
864
|
215
|
215 x 4 =
860 |
1
|
1 x 2 =
2 |
862
|
72
|
72 x 4 =
288 |
144
|
144 x 2=
288 |
576
|
Total number of cows and ducks = 216
Total number of legs if all of them are cows
= 216 x 4
= 864
Big difference in the total number of legs between the cows and the ducks
= 864 - 576
= 288
Small difference in number of legs between one cow and one duck
= 4 - 2
= 2
Number of ducks
= 288 ÷ 2
= 144
Number of cows
= 216 - 144
= 72
Answer(s): (a) 216; (b) 72
