There are a total of 710 horses, donkeys, geese and hens at a farm. The number of geese was 338 more than the number of horses. The total number of donkeys and hens was 2 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 440. How many donkeys were there in the farm?
(a)
Number of horses = 1 u
Number of donkeys and hens = 2 u
Number of geese = 1 u + 338
Total number of animals
= 1 u + 2 u + 1 u + 338
= 4 u + 338
4 u + 338 = 710
4 u = 710 - 338
4 u = 372
1 u = 372 ÷ 4 = 93
Number of donkeys and hens
= 2 u
= 2 x 93
= 186
(b)
Number of
donkeys |
Number of
donkeys' legs |
Number of
hens |
Number of
hens' legs |
Total
|
186
|
186 x 4 =
744 |
0
|
0
|
744
|
185
|
185 x 4 =
740 |
1
|
1 x 2 =
2 |
742
|
34
|
34 x 4 =
136 |
152
|
152 x 2=
304 |
440
|
Total number of donkeys and hens = 186
Total number of legs if all of them are donkeys
= 186 x 4
= 744
Big difference in the total number of legs between the donkeys and the hens
= 744 - 440
= 304
Small difference in number of legs between one donkey and one hen
= 4 - 2
= 2
Number of hens
= 304 ÷ 2
= 152
Number of donkeys
= 186 - 152
= 34
Answer(s): (a) 186; (b) 34
