Adam has a total of 20 hens and buffaloes.
The number of hens' legs is 14 less than the buffaloes' legs.
How many (a) hens and (b) buffaloes does Adam have?
| Number of buffaloes |
Number of buffaloes' legs |
Number of hens |
Number of hens' legs |
Number of less
hens' legs than buffaloes' legs |
20
|
20 x 4 =
80 |
0 |
0 x 2 =
0 |
80 - 0 =
80 |
| 19 |
19 x 4 =
76 |
1 |
1 x 2 =
2 |
76 - 2 =
74 |
| 9 |
9 x 4 =
36 |
11 |
11 x 2 =
22 |
36 - 22 =
14 |
(a)
If Adam has 20 buffaloes,
the number of legs
= 20 x 4
= 80
If Adam has 19 buffaloes and 1 hen,
number of less hens' legs than buffaloes' legs
= 19 x 4 - 1 x 2
= 76 - 2
= 74
Decrease in the number of legs when 1 buffalo is replaced by a 1 hen
= 80 - 74
= 6
Total decrease in the number of legs
= 80 - 14
= 66
Number of hens
= 66 ÷ 6
= 11
(b)
Number of buffaloes
= 20 - 11
= 9
Answer(s): (a) 11; (b) 9
