There are a total of 759 donkeys, horses, geese and hens at a farm. The number of geese was 307 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 656. How many horses were there in the farm?
(a)
Number of donkeys = 1 u
Number of horses and hens = 2 u
Number of geese = 1 u + 307
Total number of animals
= 1 u + 2 u + 1 u + 307
= 4 u + 307
4 u + 307 = 759
4 u = 759 - 307
4 u = 452
1 u = 452 ÷ 4 = 113
Number of horses and hens
= 2 u
= 2 x 113
= 226
(b)
Number of
horses |
Number of
horses' legs |
Number of
hens |
Number of
hens' legs |
Total
|
226
|
226 x 4 =
904 |
0
|
0
|
904
|
225
|
225 x 4 =
900 |
1
|
1 x 2 =
2 |
902
|
102
|
102 x 4 =
408 |
124
|
124 x 2=
248 |
656
|
Total number of horses and hens = 226
Total number of legs if all of them are horses
= 226 x 4
= 904
Big difference in the total number of legs between the horses and the hens
= 904 - 656
= 248
Small difference in number of legs between one horse and one hen
= 4 - 2
= 2
Number of hens
= 248 ÷ 2
= 124
Number of horses
= 226 - 124
= 102
Answer(s): (a) 226; (b) 102
