There are a total of 790 goats, horses, geese and hens at a farm. The number of geese was 322 more than the number of goats. The total number of horses and hens was 2 times the number of goats.
- How many horses and hens were there at the farm?
- The total number of legs for all the horses and hens was 692. How many horses were there in the farm?
(a)
Number of goats = 1 u
Number of horses and hens = 2 u
Number of geese = 1 u + 322
Total number of animals
= 1 u + 2 u + 1 u + 322
= 4 u + 322
4 u + 322 = 790
4 u = 790 - 322
4 u = 468
1 u = 468 ÷ 4 = 117
Number of horses and hens
= 2 u
= 2 x 117
= 234
(b)
Number of
horses |
Number of
horses' legs |
Number of
hens |
Number of
hens' legs |
Total
|
234
|
234 x 4 =
936 |
0
|
0
|
936
|
233
|
233 x 4 =
932 |
1
|
1 x 2 =
2 |
934
|
112
|
112 x 4 =
448 |
122
|
122 x 2=
244 |
692
|
Total number of horses and hens = 234
Total number of legs if all of them are horses
= 234 x 4
= 936
Big difference in the total number of legs between the horses and the hens
= 936 - 692
= 244
Small difference in number of legs between one horse and one hen
= 4 - 2
= 2
Number of hens
= 244 ÷ 2
= 122
Number of horses
= 234 - 122
= 112
Answer(s): (a) 234; (b) 112
