In a field of ducks and a dog someone counted 25 heads and 80 legs. How many dogs and ducks are there

Ducks have two legs while dogs have four legs and their are 25 heads, so there must be 15 dogs and 10 ducks.

15 (heads) x 4 (legs/head) = 60 legs 10 (heads) x 2 (legs/head) = 20 legs

60 legs + 20 legs = 80 legs

15 heads + 10 heads = 25 heads

(legs/head) is read as legs per head

Ducks have 1 head. Dogs have 1 head.

Ducks have 2 feet. Dogs have 4 feet.

If x = no. of ducks and g = no. of dogs

x + g = 25

2x + 4g = 80

Let's use substitution to solve.

x + g = 25 ⇒ x = 25 - g

replace x with 25 - g in the other equation and solve for g

2x + 4g = 80

2 (25 - g) + 4g = 80

50 - 2g + 4g = 80

50 + 2g = 80

2g = 30

g = 15

Now use g = 15 in an earlier equation to find x.

x + g = 25

x + 15 = 25

x = 10