There are a total of 607 donkeys, donkeys, geese and ducks at a farm. The number of geese was 382 more than the number of donkeys. The total number of donkeys and ducks was 3 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 508. How many donkeys were there in the farm?
(a)
Number of donkeys = 1 u
Number of donkeys and ducks = 3 u
Number of geese = 1 u + 382
Total number of animals
= 1 u + 3 u + 1 u + 382
= 5 u + 382
5 u + 382 = 607
5 u = 607 - 382
5 u = 225
1 u = 225 ÷ 5 = 45
Number of donkeys and ducks
= 3 u
= 3 x 45
= 135
(b)
Number of
donkeys |
Number of
donkeys' legs |
Number of
ducks |
Number of
ducks' legs |
Total
|
135
|
135 x 4 =
540 |
0
|
0
|
540
|
134
|
134 x 4 =
536 |
1
|
1 x 2 =
2 |
538
|
119
|
119 x 4 =
476 |
16
|
16 x 2=
32 |
508
|
Total number of donkeys and ducks = 135
Total number of legs if all of them are donkeys
= 135 x 4
= 540
Big difference in the total number of legs between the donkeys and the ducks
= 540 - 508
= 32
Small difference in number of legs between one donkey and one duck
= 4 - 2
= 2
Number of ducks
= 32 ÷ 2
= 16
Number of donkeys
= 135 - 16
= 119
Answer(s): (a) 135; (b) 119
