There are a total of 699 horses, donkeys, chickens and hens at a farm. The number of chickens was 387 more than the number of horses. The total number of donkeys and hens was 4 times the number of horses.
- How many donkeys and hens were there at the farm?
- The total number of legs for all the donkeys and hens was 658. How many donkeys were there in the farm?
(a)
Number of horses = 1 u
Number of donkeys and hens = 4 u
Number of chickens = 1 u + 387
Total number of animals
= 1 u + 4 u + 1 u + 387
= 6 u + 387
6 u + 387 = 699
6 u = 699 - 387
6 u = 312
1 u = 312 ÷ 6 = 52
Number of donkeys and hens
= 4 u
= 4 x 52
= 208
(b)
Number of
donkeys |
Number of
donkeys' legs |
Number of
hens |
Number of
hens' legs |
Total
|
208
|
208 x 4 =
832 |
0
|
0
|
832
|
207
|
207 x 4 =
828 |
1
|
1 x 2 =
2 |
830
|
121
|
121 x 4 =
484 |
87
|
87 x 2=
174 |
658
|
Total number of donkeys and hens = 208
Total number of legs if all of them are donkeys
= 208 x 4
= 832
Big difference in the total number of legs between the donkeys and the hens
= 832 - 658
= 174
Small difference in number of legs between one donkey and one hen
= 4 - 2
= 2
Number of hens
= 174 ÷ 2
= 87
Number of donkeys
= 208 - 87
= 121
Answer(s): (a) 208; (b) 121
