There are a total of 792 donkeys, donkeys, geese and ducks at a farm. The number of geese was 388 more than the number of donkeys. The total number of donkeys and ducks was 2 times the number of donkeys.
- How many donkeys and ducks were there at the farm?
- The total number of legs for all the donkeys and ducks was 552. How many donkeys were there in the farm?
(a)
Number of donkeys = 1 u
Number of donkeys and ducks = 2 u
Number of geese = 1 u + 388
Total number of animals
= 1 u + 2 u + 1 u + 388
= 4 u + 388
4 u + 388 = 792
4 u = 792 - 388
4 u = 404
1 u = 404 ÷ 4 = 101
Number of donkeys and ducks
= 2 u
= 2 x 101
= 202
(b)
Number of
donkeys |
Number of
donkeys' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
202
|
202 x 4 =
808 |
0
|
0
|
808
|
201
|
201 x 4 =
804 |
1
|
1 x 2 =
2 |
806
|
74
|
74 x 4 =
296 |
128
|
128 x 2=
256 |
552
|
Total number of donkeys and ducks = 202
Total number of legs if all of them are donkeys
= 202 x 4
= 808
Big difference in the total number of legs between the donkeys and the ducks
= 808 - 552
= 256
Small difference in number of legs between one donkey and one duck
= 4 - 2
= 2
Number of ducks
= 256 ÷ 2
= 128
Number of donkeys
= 202 - 128
= 74
Answer(s): (a) 202; (b) 74
