There are a total of 710 sheep, goats, geese and ducks at a farm. The number of geese was 334 more than the number of sheep. The total number of goats and ducks was 2 times the number of sheep.
- How many goats and ducks were there at the farm?
- The total number of legs for all the goats and ducks was 558. How many goats were there in the farm?
(a)
Number of sheep = 1 u
Number of goats 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 = 710
4 u = 710 - 334
4 u = 376
1 u = 376 ÷ 4 = 94
Number of goats and ducks
= 2 u
= 2 x 94
= 188
(b)
Number of
goats |
Number of
goats' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
188
|
188 x 4 =
752 |
0
|
0
|
752
|
187
|
187 x 4 =
748 |
1
|
1 x 2 =
2 |
750
|
91
|
91 x 4 =
364 |
97
|
97 x 2=
194 |
558
|
Total number of goats and ducks = 188
Total number of legs if all of them are goats
= 188 x 4
= 752
Big difference in the total number of legs between the goats and the ducks
= 752 - 558
= 194
Small difference in number of legs between one goat and one duck
= 4 - 2
= 2
Number of ducks
= 194 ÷ 2
= 97
Number of goats
= 188 - 97
= 91
Answer(s): (a) 188; (b) 91
