Question

Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and

Answer 1

Answer:

44 cows and 36 ducks.

Step-by-step explanation:

x is ducks and y is cows.

Assuming both have 1 head each, we can write:

x + y = 80.

Let's assume each x(cow) has 4 legs and each y(duck) has two legs.

Then we can add the numbers of legs:

2x + 4y = 248 legs

Now rearrange x + y = 80 to:

x = 80-y

and substitute:

2x + 4y = 248 legs

2(80-y) + 4y = 248 legs

160 - 2y + 4y = 248 legs

2y = 88 legs

y = 44   [There are 44 cows]

Use this value to find the number of ducks:

x + y = 80

44 + y = 80

y = 36  [There are 36 ducks]

========================

Check:

Do 44 cows and 36 ducks have a total of 248 legs?

4*44 + 2*36 = 248 ?

176 + 72 = 248?

YES