There are a total of 708 donkeys, pigs, geese and ducks at a farm. The number of geese was 324 more than the number of donkeys. The total number of pigs and ducks was 4 times the number of donkeys.
- How many pigs and ducks were there at the farm?
- The total number of legs for all the pigs and ducks was 692. How many pigs were there in the farm?
(a)
Number of donkeys = 1 u
Number of pigs and ducks = 4 u
Number of geese = 1 u + 324
Total number of animals
= 1 u + 4 u + 1 u + 324
= 6 u + 324
6 u + 324 = 708
6 u = 708 - 324
6 u = 384
1 u = 384 ÷ 6 = 64
Number of pigs and ducks
= 4 u
= 4 x 64
= 256
(b)
Number of
pigs |
Number of
pigs' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
256
|
256 x 4 =
1024 |
0
|
0
|
1024
|
255
|
255 x 4 =
1020 |
1
|
1 x 2 =
2 |
1022
|
90
|
90 x 4 =
360 |
166
|
166 x 2=
332 |
692
|
Total number of pigs and ducks = 256
Total number of legs if all of them are pigs
= 256 x 4
= 1024
Big difference in the total number of legs between the pigs and the ducks
= 1024 - 692
= 332
Small difference in number of legs between one pig and one duck
= 4 - 2
= 2
Number of ducks
= 332 ÷ 2
= 166
Number of pigs
= 256 - 166
= 90
Answer(s): (a) 256; (b) 90
