There are a total of 631 horses, sheep, chickens and ducks at a farm. The number of chickens was 343 more than the number of horses. The total number of sheep and ducks was 4 times the number of horses.
- How many sheep and ducks were there at the farm?
- The total number of legs for all the sheep and ducks was 634. How many sheep were there in the farm?
(a)
Number of horses = 1 u
Number of sheep and ducks = 4 u
Number of chickens = 1 u + 343
Total number of animals
= 1 u + 4 u + 1 u + 343
= 6 u + 343
6 u + 343 = 631
6 u = 631 - 343
6 u = 288
1 u = 288 ÷ 6 = 48
Number of sheep and ducks
= 4 u
= 4 x 48
= 192
(b)
Number of
sheep |
Number of
sheep' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
192
|
192 x 4 =
768 |
0
|
0
|
768
|
191
|
191 x 4 =
764 |
1
|
1 x 2 =
2 |
766
|
125
|
125 x 4 =
500 |
67
|
67 x 2=
134 |
634
|
Total number of sheep and ducks = 192
Total number of legs if all of them are sheep
= 192 x 4
= 768
Big difference in the total number of legs between the sheep and the ducks
= 768 - 634
= 134
Small difference in number of legs between one sheep and one duck
= 4 - 2
= 2
Number of ducks
= 134 ÷ 2
= 67
Number of sheep
= 192 - 67
= 125
Answer(s): (a) 192; (b) 125
