Question

A farmer raises only ducks and pigs. There are 55 animals in all on his farm, and 146 legs.

Find the number of ducks and pigs on his farm by setting up and solving a system of equations.
Define the variables
Equations
Show all work

Answer 1

Number of ducks = 37

Number of pigs = 18

Explanation:

Let,

x be the number of ducks

y be the number of pigs

According to given statement;

x+y=55 Eqn 1

2x+4y=146 Eqn 2 (As ducks will have 2 legs and pigs will have 4)

Multiplying Eqn 1 by 2

2(x+y=55)

2x+2y=110 Eqn 3

Subtracting Eqn 3 from Eqn 2

(2x+4y)-(2x+2y)=146-110

2x+4y-2x-2y=36

2y=36

Dividing both sides by 2

`(2y)/(2)=(36)/(2)\\y=18`

Putting y=18 in Eqn 1

x+18=55

x = 55-18

x = 37

Hence,

Number of ducks = 37

Number of pigs = 18