Question

Farmer Mike wants to know how many cows and ducks are in the meadow. After counting 56 legs and 17 heads the farmer knows. How many cows and ducks are there in the meadow?

Answer 1

There 11 cows and 6 ducks in the meadow.

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;

`c+d=17\ \ \ \ equation\ 1`

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;

`4c+2d=56`

On dividing both side by '2' using division property, we get;

`(4c+2d)/(2)=(56)/(2)\\\\2c+d=28\ \ \ \ equation\ 2`

Now Subtracting equation 1 from equation 2 we get;

`2c+d-(c+d)=28-17\\\\2c+d-c-d=11\\\\c=11`

Substituting the value of c in equation 1 we get;

`c+d=17\\\\11+d=17\\\\d=17-11=6`

Hence There 11 cows and 6 ducks in the meadow.