There are a total of 675 cows, horses, hens and geese at a farm. The number of hens was 400 more than the number of cows. The total number of horses and geese was 3 times the number of cows.
- How many horses and geese were there at the farm?
- The total number of legs for all the horses and geese was 616. How many horses were there in the farm?
(a)
Number of cows = 1 u
Number of horses and geese = 3 u
Number of hens = 1 u + 400
Total number of animals
= 1 u + 3 u + 1 u + 400
= 5 u + 400
5 u + 400 = 675
5 u = 675 - 400
5 u = 275
1 u = 275 ÷ 5 = 55
Number of horses and geese
= 3 u
= 3 x 55
= 165
(b)
Number of
horses |
Number of
horses' legs |
Number of
geese |
Number of
geese' legs |
Total
|
165
|
165 x 4 =
660 |
0
|
0
|
660
|
164
|
164 x 4 =
656 |
1
|
1 x 2 =
2 |
658
|
143
|
143 x 4 =
572 |
22
|
22 x 2=
44 |
616
|
Total number of horses and geese = 165
Total number of legs if all of them are horses
= 165 x 4
= 660
Big difference in the total number of legs between the horses and the geese
= 660 - 616
= 44
Small difference in number of legs between one horse and one goose
= 4 - 2
= 2
Number of geese
= 44 ÷ 2
= 22
Number of horses
= 165 - 22
= 143
Answer(s): (a) 165; (b) 143
