There are a total of 643 pigs, donkeys, chickens and hens at a farm. The number of chickens was 367 more than the number of pigs. The total number of donkeys and hens was 4 times the number of pigs.
- How many donkeys and hens were there at the farm?
- The total number of legs for all the donkeys and hens was 428. How many donkeys were there in the farm?
(a)
Number of pigs = 1 u
Number of donkeys and hens = 4 u
Number of chickens = 1 u + 367
Total number of animals
= 1 u + 4 u + 1 u + 367
= 6 u + 367
6 u + 367 = 643
6 u = 643 - 367
6 u = 276
1 u = 276 ÷ 6 = 46
Number of donkeys and hens
= 4 u
= 4 x 46
= 184
(b)
Number of
donkeys |
Number of
donkeys' legs |
Number of
hens |
Number of
hens' legs |
Total
|
184
|
184 x 4 =
736 |
0
|
0
|
736
|
183
|
183 x 4 =
732 |
1
|
1 x 2 =
2 |
734
|
30
|
30 x 4 =
120 |
154
|
154 x 2=
308 |
428
|
Total number of donkeys and hens = 184
Total number of legs if all of them are donkeys
= 184 x 4
= 736
Big difference in the total number of legs between the donkeys and the hens
= 736 - 428
= 308
Small difference in number of legs between one donkey and one hen
= 4 - 2
= 2
Number of hens
= 308 ÷ 2
= 154
Number of donkeys
= 184 - 154
= 30
Answer(s): (a) 184; (b) 30
