There are a total of 688 donkeys, pigs, chickens and hens at a farm. The number of chickens was 328 more than the number of donkeys. The total number of pigs and hens was 2 times the number of donkeys.
- How many pigs and hens were there at the farm?
- The total number of legs for all the pigs and hens was 592. How many pigs were there in the farm?
(a)
Number of donkeys = 1 u
Number of pigs and hens = 2 u
Number of chickens = 1 u + 328
Total number of animals
= 1 u + 2 u + 1 u + 328
= 4 u + 328
4 u + 328 = 688
4 u = 688 - 328
4 u = 360
1 u = 360 ÷ 4 = 90
Number of pigs and hens
= 2 u
= 2 x 90
= 180
(b)
Number of
pigs |
Number of
pigs' legs |
Number of
hens |
Number of
hens' legs |
Total
|
180
|
180 x 4 =
720 |
0
|
0
|
720
|
179
|
179 x 4 =
716 |
1
|
1 x 2 =
2 |
718
|
116
|
116 x 4 =
464 |
64
|
64 x 2=
128 |
592
|
Total number of pigs and hens = 180
Total number of legs if all of them are pigs
= 180 x 4
= 720
Big difference in the total number of legs between the pigs and the hens
= 720 - 592
= 128
Small difference in number of legs between one pig and one hen
= 4 - 2
= 2
Number of hens
= 128 ÷ 2
= 64
Number of pigs
= 180 - 64
= 116
Answer(s): (a) 180; (b) 116
