There are a total of 762 buffaloes, pigs, geese and ducks at a farm. The number of geese was 334 more than the number of buffaloes. The total number of pigs and ducks was 2 times the number of buffaloes.
- How many pigs and ducks were there at the farm?
- The total number of legs for all the pigs and ducks was 550. How many pigs were there in the farm?
(a)
Number of buffaloes = 1 u
Number of pigs and ducks = 2 u
Number of geese = 1 u + 334
Total number of animals
= 1 u + 2 u + 1 u + 334
= 4 u + 334
4 u + 334 = 762
4 u = 762 - 334
4 u = 428
1 u = 428 ÷ 4 = 107
Number of pigs and ducks
= 2 u
= 2 x 107
= 214
(b)
Number of
pigs |
Number of
pigs' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
214
|
214 x 4 =
856 |
0
|
0
|
856
|
213
|
213 x 4 =
852 |
1
|
1 x 2 =
2 |
854
|
61
|
61 x 4 =
244 |
153
|
153 x 2=
306 |
550
|
Total number of pigs and ducks = 214
Total number of legs if all of them are pigs
= 214 x 4
= 856
Big difference in the total number of legs between the pigs and the ducks
= 856 - 550
= 306
Small difference in number of legs between one pig and one duck
= 4 - 2
= 2
Number of ducks
= 306 ÷ 2
= 153
Number of pigs
= 214 - 153
= 61
Answer(s): (a) 214; (b) 61
