There are a total of 780 pigs, buffaloes, ducks and chickens at a farm. The number of ducks was 352 more than the number of pigs. The total number of buffaloes and chickens was 2 times the number of pigs.
- How many buffaloes and chickens were there at the farm?
- The total number of legs for all the buffaloes and chickens was 564. How many buffaloes were there in the farm?
(a)
Number of pigs = 1 u
Number of buffaloes and chickens = 2 u
Number of ducks = 1 u + 352
Total number of animals
= 1 u + 2 u + 1 u + 352
= 4 u + 352
4 u + 352 = 780
4 u = 780 - 352
4 u = 428
1 u = 428 ÷ 4 = 107
Number of buffaloes and chickens
= 2 u
= 2 x 107
= 214
(b)
Number of
buffaloes |
Number of
buffaloes' legs |
Number of
chickens |
Number of
chickens' legs |
Total
|
214
|
214 x 4 =
856 |
0
|
0
|
856
|
213
|
213 x 4 =
852 |
1
|
1 x 2 =
2 |
854
|
68
|
68 x 4 =
272 |
146
|
146 x 2=
292 |
564
|
Total number of buffaloes and chickens = 214
Total number of legs if all of them are buffaloes
= 214 x 4
= 856
Big difference in the total number of legs between the buffaloes and the chickens
= 856 - 564
= 292
Small difference in number of legs between one buffalo and one chicken
= 4 - 2
= 2
Number of chickens
= 292 ÷ 2
= 146
Number of buffaloes
= 214 - 146
= 68
Answer(s): (a) 214; (b) 68
