Question

There are some ducks and goats in a field, together with 77 heads and 224 feet, the number of ducks is a)42 b)30 c)32 d)47. Explain in step by step​

Answer 1

Answer:

Step-by-step explanation:

Number of ducks is 42

Answer 2

The correct option is option (a) 42 ducks.

Given,

The number of heads of ducks and goats is 77 heads.

The number of feet of ducks and goats is 224 heads.

Let the number of ducks be $x$ and the number of goats be $y$.

The number if feet of a duck is 2 and the number of feet of a goat is 4.

Therefore, we get the equations

$x+y=77 ............(1)\\2x+4y=224 ..........(2)$

From equation (1), we get

$x+y=77\\\Rightarrow y=77-x$...................(3)

Substituting equation (3) in equation (2) and we get

$2x+4 \times (77-x)=224\\\Rightarrow 2x+308-4x=224\\\Rightarrow 2x-4x=224-308\\\Rightarrow -2x=-84\\\Rightarrow x=\frac{-84}{-2}\\\Rightarrow x=42$

Therefore, the number of ducks is 42.

Hence, option (a) is the correct option.

To learn more about the substitution process of the linear equations from the given link

https://brainly.in/question/18020417

https://brainly.in/question/32434693

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