There are a total of 787 goats, donkeys, chickens and ducks at a farm. The number of chickens was 397 more than the number of goats. The total number of donkeys and ducks was 3 times the number of goats.
- How many donkeys and ducks were there at the farm?
- The total number of legs for all the donkeys and ducks was 542. How many donkeys were there in the farm?
(a)
Number of goats = 1 u
Number of donkeys and ducks = 3 u
Number of chickens = 1 u + 397
Total number of animals
= 1 u + 3 u + 1 u + 397
= 5 u + 397
5 u + 397 = 787
5 u = 787 - 397
5 u = 390
1 u = 390 ÷ 5 = 78
Number of donkeys and ducks
= 3 u
= 3 x 78
= 234
(b)
Number of
donkeys |
Number of
donkeys' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
234
|
234 x 4 =
936 |
0
|
0
|
936
|
233
|
233 x 4 =
932 |
1
|
1 x 2 =
2 |
934
|
37
|
37 x 4 =
148 |
197
|
197 x 2=
394 |
542
|
Total number of donkeys and ducks = 234
Total number of legs if all of them are donkeys
= 234 x 4
= 936
Big difference in the total number of legs between the donkeys and the ducks
= 936 - 542
= 394
Small difference in number of legs between one donkey and one duck
= 4 - 2
= 2
Number of ducks
= 394 ÷ 2
= 197
Number of donkeys
= 234 - 197
= 37
Answer(s): (a) 234; (b) 37
