A farmer notes that in a field full of goats and ducks there are 29 heads and 82 feet how many of each animal are there

Question

i tried to use variables but I am not good at math and this problem and problems like this are very frustrating for me please help me your help would be greatly appreciated

Answer 1

Use the following facts to build two equations: 29 heads = 29 animals, goats have 4 feet, and ducks have two feet.

29 = G + D (where G = goats and D = ducks)

82 = 4G + 2D (where 4 and 2 represent the number of feet of goats and ducks respectively)

Rearrange first equation in order to substitute for one variable in the second equation:

29 = G + D --> G = 29 - D

82 = 4(29 - D) + 2D

Distribute and simplify:

82 = 116 - 4D + 2D

82 = 116 - 2D

2D = 34

D = 17

Now substitute the D value into the rearranged first equation:

G = 29 - 17

G = 12

There are 17 ducks and 12 goats.