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

Let us assume number of specimens of early birds of 2 wings = x

Total number of birds specimens = 2008.

Number of birds specimens of 4 wings = Total specimens - number of specimens of 2 wings.

Therefore,

Number of birds specimens of 4 wings = (2008 -x).

Total number of wings = 4038 wings.

We can setup an equation by statement

2*(number of specimens of 2 wings)+4*(Number of birds specimens of 4 wings) = 4038

2(x) + 4(2008-x) = 4038.

Distributing 4 over (2008-x), we get

2x + 8032 - 4x = 4038.

Combining like terms 2x-4x, we get -2x.

Therefore,

2x + 8032 - 4x = 4038

=> -2x +8032 = 4038

Subtracting 8032 from both sides, we get

-2x +8032-8032 = 4038-8032

-2x = -3994

Dividing both sides by -2, we get

-2x/-2 = -3994/-2

x=1997.

Number of birds specimens of 4 wings = 2008-x = 2008-1997 =11.

Therefore, 2 wings specimens bird are 1997 and 4 wings specimens bird are 11.

Answer 2

There are 1997 specimens with 2 wings and 11 specimens with 4 wings.

Step-by-step explanation

Suppose, the number of specimens with 2 wings is
`x`

As the museum has total 2008 specimens, so the number of specimens with 4 wings will be:
`(2008-x)`

Given that, the specimens have a total of 4038 wings. So, the equation will be.....

`2(x)+4(2008-x)=4038\\ \\ 2x+8032-4x=4038\\ \\ -2x=4038-8032\\ \\ -2x=-3994\\ \\ x=(-3994)/(-2)=1997`

So, the number of specimens with 2 wings is 1997

and the number of specimens with 4 wings is (2008-1997) = 11