Adam has a total of 12 ducks and cows.
The number of ducks' legs is 24 less than the cows' legs.
How many (a) ducks and (b) cows does Adam have?
| Number of cows |
Number of cows' legs |
Number of ducks |
Number of ducks' legs |
Number of less
ducks' legs than cows' legs |
12
|
12 x 4 =
48 |
0 |
0 x 2 =
0 |
48 - 0 =
48 |
| 11 |
11 x 4 =
44 |
1 |
1 x 2 =
2 |
44 - 2 =
42 |
| 8 |
8 x 4 =
32 |
4 |
4 x 2 =
8 |
32 - 8 =
24 |
(a)
If Adam has 12 cows,
the number of legs
= 12 x 4
= 48
If Adam has 11 cows and 1 duck,
number of less ducks' legs than cows' legs
= 11 x 4 - 1 x 2
= 44 - 2
= 42
Decrease in the number of legs when 1 cow is replaced by a 1 duck
= 48 - 42
= 6
Total decrease in the number of legs
= 48 - 24
= 24
Number of ducks
= 24 ÷ 6
= 4
(b)
Number of cows
= 12 - 4
= 8
Answer(s): (a) 4; (b) 8
