There are a total of 624 donkeys, sheep, geese and hens at a farm. The number of geese was 314 more than the number of donkeys. The total number of sheep and hens was 3 times the number of donkeys.
- How many sheep and hens were there at the farm?
- The total number of legs for all the sheep and hens was 692. How many sheep were there in the farm?
(a)
Number of donkeys = 1 u
Number of sheep and hens = 3 u
Number of geese = 1 u + 314
Total number of animals
= 1 u + 3 u + 1 u + 314
= 5 u + 314
5 u + 314 = 624
5 u = 624 - 314
5 u = 310
1 u = 310 ÷ 5 = 62
Number of sheep and hens
= 3 u
= 3 x 62
= 186
(b)
Number of
sheep |
Number of
sheep' legs |
Number of
hens |
Number of
hens' legs |
Total
|
186
|
186 x 4 =
744 |
0
|
0
|
744
|
185
|
185 x 4 =
740 |
1
|
1 x 2 =
2 |
742
|
160
|
160 x 4 =
640 |
26
|
26 x 2=
52 |
692
|
Total number of sheep and hens = 186
Total number of legs if all of them are sheep
= 186 x 4
= 744
Big difference in the total number of legs between the sheep and the hens
= 744 - 692
= 52
Small difference in number of legs between one sheep and one hen
= 4 - 2
= 2
Number of hens
= 52 ÷ 2
= 26
Number of sheep
= 186 - 26
= 160
Answer(s): (a) 186; (b) 160
