There are a total of 622 donkeys, horses, chickens and ducks at a farm. The number of chickens was 387 more than the number of donkeys. The total number of horses and ducks was 3 times the number of donkeys.
- How many horses and ducks were there at the farm?
- The total number of legs for all the horses and ducks was 448. How many horses were there in the farm?
(a)
Number of donkeys = 1 u
Number of horses and ducks = 3 u
Number of chickens = 1 u + 387
Total number of animals
= 1 u + 3 u + 1 u + 387
= 5 u + 387
5 u + 387 = 622
5 u = 622 - 387
5 u = 235
1 u = 235 ÷ 5 = 47
Number of horses and ducks
= 3 u
= 3 x 47
= 141
(b)
Number of
horses |
Number of
horses' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
141
|
141 x 4 =
564 |
0
|
0
|
564
|
140
|
140 x 4 =
560 |
1
|
1 x 2 =
2 |
562
|
83
|
83 x 4 =
332 |
58
|
58 x 2=
116 |
448
|
Total number of horses and ducks = 141
Total number of legs if all of them are horses
= 141 x 4
= 564
Big difference in the total number of legs between the horses and the ducks
= 564 - 448
= 116
Small difference in number of legs between one horse and one duck
= 4 - 2
= 2
Number of ducks
= 116 ÷ 2
= 58
Number of horses
= 141 - 58
= 83
Answer(s): (a) 141; (b) 83
