There are a total of 621 donkeys, horses, hens and geese at a farm. The number of hens was 365 more than the number of donkeys. The total number of horses and geese was 2 times the number of donkeys.
- How many horses and geese were there at the farm?
- The total number of legs for all the horses and geese was 416. How many horses were there in the farm?
(a)
Number of donkeys = 1 u
Number of horses and geese = 2 u
Number of hens = 1 u + 365
Total number of animals
= 1 u + 2 u + 1 u + 365
= 4 u + 365
4 u + 365 = 621
4 u = 621 - 365
4 u = 256
1 u = 256 ÷ 4 = 64
Number of horses and geese
= 2 u
= 2 x 64
= 128
(b)
Number of
horses |
Number of
horses' legs |
Number of
geese |
Number of
geese' legs |
Total
|
128
|
128 x 4 =
512 |
0
|
0
|
512
|
127
|
127 x 4 =
508 |
1
|
1 x 2 =
2 |
510
|
80
|
80 x 4 =
320 |
48
|
48 x 2=
96 |
416
|
Total number of horses and geese = 128
Total number of legs if all of them are horses
= 128 x 4
= 512
Big difference in the total number of legs between the horses and the geese
= 512 - 416
= 96
Small difference in number of legs between one horse and one goose
= 4 - 2
= 2
Number of geese
= 96 ÷ 2
= 48
Number of horses
= 128 - 48
= 80
Answer(s): (a) 128; (b) 80
