Question

A nature museum has 2008 specimens of early birds, some with 2 wings and some with 4 wings. The specimens have a total of 4038 wings. How many specimens are there with each number of wings?

Answer 1

If each bird had two wings, there would be 4016 wings. For each two-winged bird we replace with a four-winged bird, the total number of wings would increase by 2. We need 22 more wings, so 11 two-winged birds need to be replaced by four-winged birds. Thus, there are 1997 two-winged and 11 four winged birds.

Answer 2

• 1997 birds has 2 wings

• 11 birds has 4 wings

Explanation:

Given :

Number of specimens in the museum =2008 specimens of early birds, Some with 2 wings and some with 4 wings.

Total number of wings the specimen have=4038

To Find:

Number of birds with 2 wings=?

Number of birds with 4 wings=?

Solution:

Let the number of birds with 2 wings be n,

then number of birds with 4 wings will be 2008 – n birds.

Now, total number of wings = 4038 wings

=>2 wings x number of birds with 2 wings + 4 wings x number of birds with 4 wings = 4038 wings

=> 2 x n + 4 x (2008 – n) = 4038

=>2n + 4 x 2008 – 4n = 4038

=>2n + 8032 – 4n = 4038

=>2n – 4n = 4038 – 8032

=>- 2n = - 3994

=>2n = 3994

=>
`n=(3994)/(2)`

=>n = 1997

So, 1997 birds has 2 wings, then, 2008 – 1997 = 11 birds has 4 wings.