There are a total of 748 sheep, donkeys, hens and ducks at a farm. The number of hens was 358 more than the number of sheep. The total number of donkeys and ducks was 4 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 540. How many donkeys were there in the farm?
(a)
Number of sheep = 1 u
Number of donkeys and ducks = 4 u
Number of hens = 1 u + 358
Total number of animals
= 1 u + 4 u + 1 u + 358
= 6 u + 358
6 u + 358 = 748
6 u = 748 - 358
6 u = 390
1 u = 390 ÷ 6 = 65
Number of donkeys and ducks
= 4 u
= 4 x 65
= 260
(b)
Number of
donkeys |
Number of
donkeys' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
260
|
260 x 4 =
1040 |
0
|
0
|
1040
|
259
|
259 x 4 =
1036 |
1
|
1 x 2 =
2 |
1038
|
10
|
10 x 4 =
40 |
250
|
250 x 2=
500 |
540
|
Total number of donkeys and ducks = 260
Total number of legs if all of them are donkeys
= 260 x 4
= 1040
Big difference in the total number of legs between the donkeys and the ducks
= 1040 - 540
= 500
Small difference in number of legs between one donkey and one duck
= 4 - 2
= 2
Number of ducks
= 500 ÷ 2
= 250
Number of donkeys
= 260 - 250
= 10
Answer(s): (a) 260; (b) 10
