Question

Old Mc Donald raises ducks and cows. The animals have a total of 100 heads and 354 feet. How many ducks and how many cows does Old Mc Donald have?

Answer 1

The number of ducks Old Mc Donald raises are 23 and the number of cows Old Mc Donald raises are 77.

Explanation:

We are given that Old Mc Donald raises ducks and cows. The animals have a total of 100 heads and 354 feet.

Let the number of ducks Old Mc Donald raises be 'x' and the number of cows Old Mc Donald raises be 'y'.

So, according to the question;

• The first condition states that the animals have a total of 100 heads, that means;

`x+y=100`

`x=100-y` -------------------- [equation 1]

{because one head of a duck and one head of cow}

• The second condition states that the animals have a total of 354 feet, that means;

`2x+4y=354`

`x+2y=177` --------------- [equation 2]

{because there are two feet of a duck and four feet of cow}

Now, putting the value of x in equation 2 we get;

`100-y+2y=177`

`y=177-100`

y = 77 cows

Putting this value of y in equation 1 we get;

x = 100 - y

x = 100 - 77 = 23 ducks

Hence, the number of ducks Old Mc Donald raises are 23 and the number of cows Old Mc Donald raises are 77.