There are a total of 632 sheep, donkeys, chickens and ducks at a farm. The number of chickens was 380 more than the number of sheep. The total number of donkeys and ducks was 4 times the number of sheep.
- How many donkeys and ducks were there at the farm?
- The total number of legs for all the donkeys and ducks was 430. How many donkeys were there in the farm?
(a)
Number of sheep = 1 u
Number of donkeys and ducks = 4 u
Number of chickens = 1 u + 380
Total number of animals
= 1 u + 4 u + 1 u + 380
= 6 u + 380
6 u + 380 = 632
6 u = 632 - 380
6 u = 252
1 u = 252 ÷ 6 = 42
Number of donkeys and ducks
= 4 u
= 4 x 42
= 168
(b)
Number of donkeys |
Number of donkeys' legs |
Number of ducks |
Number of ducks' legs |
Total
|
168
|
168 x 4 = 672 |
0
|
0
|
672
|
167
|
167 x 4 = 668 |
1
|
1 x 2 = 2 |
670
|
47
|
47 x 4 = 188 |
121
|
121 x 2= 242 |
430
|
Total number of donkeys and ducks = 168
Total number of legs if all of them are donkeys
= 168 x 4
= 672
Big difference in the total number of legs between the donkeys and the ducks
= 672 - 430
= 242
Small difference in number of legs between one donkey and one duck
= 4 - 2
= 2
Number of ducks
= 242 ÷ 2
= 121
Number of donkeys
= 168 - 121
= 47
Answer(s): (a) 168; (b) 47