Adam has a total of 15 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 |
15
|
15 x 4 = 60 |
0 |
0 x 2 = 0 |
60 - 0 = 60 |
14 |
14 x 4 = 56 |
1 |
1 x 2 = 2 |
56 - 2 = 54 |
9 |
9 x 4 = 36 |
6 |
6 x 2 = 12 |
36 - 12 = 24 |
(a)
If Adam has 15 cows,
the number of legs
= 15 x 4
= 60
If Adam has 14 cows and 1 duck,
number of less ducks' legs than cows' legs
= 14 x 4 - 1 x 2
= 56 - 2
= 54
Decrease in the number of legs when 1 cow is replaced by a 1 duck
= 60 - 54
= 6
Total decrease in the number of legs
= 60 - 24
= 36
Number of ducks
= 36 ÷ 6
= 6
(b)
Number of cows
= 15 - 6
= 9
Answer(s): (a) 6; (b) 9