Respuesta :
Answer:
There 11 cows and 6 ducks in the meadow.
Step-by-step explanation:
Given,
Total number of legs = 56
Total number of heads = 17
Solution,
Let the number of cows be 'c'.
And also let the number of ducks be 'd'.
We know that all the animals have 1 head.
So we can say that the total number of heads is equal to number of number of cows and number of ducks.
we can frame it as;
[tex]c+d=17\ \ \ \ equation\ 1[/tex]
Again we know that cows have four legs and ducks have two legs.
So total number of legs is equal to number of cows multiplied by 4 plus number of ducks multiplied by 2.
framing in equation form, we get;
[tex]4c+2d=56[/tex]
On dividing both side by '2' using division property, we get;
[tex]\frac{4c+2d}{2}=\frac{56}{2}\\\\2c+d=28\ \ \ \ equation\ 2[/tex]
Now Subtracting equation 1 from equation 2 we get;
[tex]2c+d-(c+d)=28-17\\\\2c+d-c-d=11\\\\c=11[/tex]
Substituting the value of c in equation 1 we get;
[tex]c+d=17\\\\11+d=17\\\\d=17-11=6[/tex]
Hence There 11 cows and 6 ducks in the meadow.
