There are a total of 795 donkeys, horses, ducks and hens at a farm. The number of ducks was 363 more than the number of donkeys. The total number of horses and hens was 2 times the number of donkeys.
- How many horses and hens were there at the farm?
- The total number of legs for all the horses and hens was 658. How many horses were there in the farm?
(a)
Number of donkeys = 1 u
Number of horses and hens = 2 u
Number of ducks = 1 u + 363
Total number of animals
= 1 u + 2 u + 1 u + 363
= 4 u + 363
4 u + 363 = 795
4 u = 795 - 363
4 u = 432
1 u = 432 ÷ 4 = 108
Number of horses and hens
= 2 u
= 2 x 108
= 216
(b)
Number of
horses |
Number of
horses' legs |
Number of
hens |
Number of
hens' legs |
Total
|
216
|
216 x 4 =
864 |
0
|
0
|
864
|
215
|
215 x 4 =
860 |
1
|
1 x 2 =
2 |
862
|
113
|
113 x 4 =
452 |
103
|
103 x 2=
206 |
658
|
Total number of horses and hens = 216
Total number of legs if all of them are horses
= 216 x 4
= 864
Big difference in the total number of legs between the horses and the hens
= 864 - 658
= 206
Small difference in number of legs between one horse and one hen
= 4 - 2
= 2
Number of hens
= 206 ÷ 2
= 103
Number of horses
= 216 - 103
= 113
Answer(s): (a) 216; (b) 113
