There are a total of 686 cows, horses, chickens and geese at a farm. The number of chickens was 366 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 646. How many horses were there in the farm?
(a)
Number of cows = 1 u
Number of horses and geese = 3 u
Number of chickens = 1 u + 366
Total number of animals
= 1 u + 3 u + 1 u + 366
= 5 u + 366
5 u + 366 = 686
5 u = 686 - 366
5 u = 320
1 u = 320 ÷ 5 = 64
Number of horses and geese
= 3 u
= 3 x 64
= 192
(b)
Number of
horses |
Number of
horses' legs |
Number of
geese |
Number of
geese' legs |
Total
|
192
|
192 x 4 =
768 |
0
|
0
|
768
|
191
|
191 x 4 =
764 |
1
|
1 x 2 =
2 |
766
|
131
|
131 x 4 =
524 |
61
|
61 x 2=
122 |
646
|
Total number of horses and geese = 192
Total number of legs if all of them are horses
= 192 x 4
= 768
Big difference in the total number of legs between the horses and the geese
= 768 - 646
= 122
Small difference in number of legs between one horse and one goose
= 4 - 2
= 2
Number of geese
= 122 ÷ 2
= 61
Number of horses
= 192 - 61
= 131
Answer(s): (a) 192; (b) 131
