There are a total of 613 cows, sheep, chickens and ducks at a farm. The number of chickens was 301 more than the number of cows. The total number of sheep and ducks was 2 times the number of cows.
- How many sheep and ducks were there at the farm?
- The total number of legs for all the sheep and ducks was 452. How many sheep were there in the farm?
(a)
Number of cows = 1 u
Number of sheep and ducks = 2 u
Number of chickens = 1 u + 301
Total number of animals
= 1 u + 2 u + 1 u + 301
= 4 u + 301
4 u + 301 = 613
4 u = 613 - 301
4 u = 312
1 u = 312 ÷ 4 = 78
Number of sheep and ducks
= 2 u
= 2 x 78
= 156
(b)
Number of
sheep |
Number of
sheep' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
156
|
156 x 4 =
624 |
0
|
0
|
624
|
155
|
155 x 4 =
620 |
1
|
1 x 2 =
2 |
622
|
70
|
70 x 4 =
280 |
86
|
86 x 2=
172 |
452
|
Total number of sheep and ducks = 156
Total number of legs if all of them are sheep
= 156 x 4
= 624
Big difference in the total number of legs between the sheep and the ducks
= 624 - 452
= 172
Small difference in number of legs between one sheep and one duck
= 4 - 2
= 2
Number of ducks
= 172 ÷ 2
= 86
Number of sheep
= 156 - 86
= 70
Answer(s): (a) 156; (b) 70
