Question

14 Some goats and ducks are grazing in a field when counted there were 34 heads and 102 legs Find the number of goats and ducks.​

Answer 1

Answer:

There are 17 goats and 17 ducks grazing in the field

Step-by-step explanation:

Let the number of goats be x and the number of ducks be y,

We know there are a total of 34 heads, so

x + y = 34

So we can also say,

No. of ducks = y = (34 - x)

Goats have 4 legs while ducks have 2 legs,

We know the total number of legs is 102,

So, 4x + 2y = 102

Or, 4x + 2(34-x) = 102

Or, 4x + 68 - 2x = 102

Or, 2x = 102 - 68

Or, 2x = 34

Therefore, x = 34/2 = 17

So number of goats = x = 17

And number of ducks = y = 34-x = 34-17 = 17

Hope this explanation helped you :D

Answer 2

Step-by-step explanation:

let number of goats = g

number of ducks = d

number of heads = g+d= 34----->i

number of legs = 4×g+ 2×d = 102---->ii

equation ii - 2 × equation I

4g +2d = 102

2g + 2d = 68

--------------------

2 g = 34

---------------------

g= 34/2

g= 17

from equation I 17+ d = 34

d= 34 - 17=17

number of ducks= d= 17

number of goats= g = 17