There are a total of 726 donkeys, goats, hens and ducks at a farm. The number of hens was 321 more than the number of donkeys. The total number of goats and ducks was 3 times the number of donkeys.
- How many goats and ducks were there at the farm?
- The total number of legs for all the goats and ducks was 572. How many goats were there in the farm?
(a)
Number of donkeys = 1 u
Number of goats and ducks = 3 u
Number of hens = 1 u + 321
Total number of animals
= 1 u + 3 u + 1 u + 321
= 5 u + 321
5 u + 321 = 726
5 u = 726 - 321
5 u = 405
1 u = 405 ÷ 5 = 81
Number of goats and ducks
= 3 u
= 3 x 81
= 243
(b)
Number of
goats |
Number of
goats' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
243
|
243 x 4 =
972 |
0
|
0
|
972
|
242
|
242 x 4 =
968 |
1
|
1 x 2 =
2 |
970
|
43
|
43 x 4 =
172 |
200
|
200 x 2=
400 |
572
|
Total number of goats and ducks = 243
Total number of legs if all of them are goats
= 243 x 4
= 972
Big difference in the total number of legs between the goats and the ducks
= 972 - 572
= 400
Small difference in number of legs between one goat and one duck
= 4 - 2
= 2
Number of ducks
= 400 ÷ 2
= 200
Number of goats
= 243 - 200
= 43
Answer(s): (a) 243; (b) 43
