Question

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

Answer 1

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

Answer 2

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