There are some cows and ducks in a park. The total number of heads of the cows…
2024
There are some cows and ducks in a park. The total number of heads of the cows and ducks is 60, while their total number of legs is 180. Find the numbers of cows and ducks in the park, respectively.
Answer: A. 30, 30 — ConceptWhen two types of objects have different per-item contributions, let their counts be variables. One equation represents the total number of objects,…
- A.
30, 30
- B.
32, 28
- C.
28, 32
- D.
24, 36
Show answer & explanation
Correct answer: A
Concept
When two types of objects have different per-item contributions, let their counts be variables. One equation represents the total number of objects, and another represents the total contribution.
Application
Let c be the number of cows and d be the number of ducks. The head count gives c + d = 60.
Each cow has 4 legs and each duck has 2 legs, so the leg count gives 4c + 2d = 180.
Divide the second equation by 2: 2c + d = 90. Subtract c + d = 60 from it to obtain c = 30.
Substitute c = 30 into c + d = 60 to obtain d = 30.
Cross-check
With 30 cows and 30 ducks, the number of heads is 30 + 30 = 60 and the number of legs is 4 × 30 + 2 × 30 = 180.
Result
Therefore, the park has 30 cows and 30 ducks, respectively.