Adam has a total of 13 ducks and cows.
The number of cows' legs is 28 more than the ducks' 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 more
cows' legs than ducks' legs |
13
|
13 x 4 =
52 |
0 |
0 x 2 =
0 |
52 - 0 =
52 |
| 12 |
12 x 4 =
48 |
1 |
1 x 2 =
2 |
48 - 2 =
46 |
| 9 |
9 x 4 =
36 |
4 |
4 x 2 =
8 |
36 - 8 =
28 |
(a)
If Adam has 13 cows,
the number of legs
= 13 x 4
= 52
If Adam has 12 cows and 1 duck,
number of more cows' legs than ducks' legs
= 12 x 4 - 1 x 2
= 48 - 2
= 46
Decrease in the number of legs when 1 cow is replaced by 1 duck
= 52 - 46
= 6
Total decrease in the number of legs
= 52 - 28
= 24
Number of ducks
= 24 ÷ 6
= 4
(b)
Number of cows
= 13 - 4
= 9
Answer(s): (a) 4; (b) 9
