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

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

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