There are a total of 603 buffaloes, cows, chickens and ducks at a farm. The number of chickens was 357 more than the number of buffaloes. The total number of cows and ducks was 4 times the number of buffaloes.
- How many cows and ducks were there at the farm?
- The total number of legs for all the cows and ducks was 432. How many cows were there in the farm?
(a)
Number of buffaloes = 1 u
Number of cows and ducks = 4 u
Number of chickens = 1 u + 357
Total number of animals
= 1 u + 4 u + 1 u + 357
= 6 u + 357
6 u + 357 = 603
6 u = 603 - 357
6 u = 246
1 u = 246 ÷ 6 = 41
Number of cows and ducks
= 4 u
= 4 x 41
= 164
(b)
Number of
cows |
Number of
cows' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
164
|
164 x 4 =
656 |
0
|
0
|
656
|
163
|
163 x 4 =
652 |
1
|
1 x 2 =
2 |
654
|
52
|
52 x 4 =
208 |
112
|
112 x 2=
224 |
432
|
Total number of cows and ducks = 164
Total number of legs if all of them are cows
= 164 x 4
= 656
Big difference in the total number of legs between the cows and the ducks
= 656 - 432
= 224
Small difference in number of legs between one cow and one duck
= 4 - 2
= 2
Number of ducks
= 224 ÷ 2
= 112
Number of cows
= 164 - 112
= 52
Answer(s): (a) 164; (b) 52
