Question

the number of ducks and pigs in a field totals 38 the number of legs among them is 94 assuming each duck has exactly two legs and each Pig has exactly four legs determine how many ducks and how many pigs are in the field

Answer 1

Let number of ducks is:

`x`

Number of pigs is:

`y`

Total number in field is 38

that mean:

`\begin{gathered} x+y=38 \\ x=38-y \end{gathered}`

Total legs is 94

Duck legs is:

`2x`

Pigs legs is:

`4y`

when total leg is 94 that mean:

`\begin{gathered} 2x+4y=94 \\ 2(x+2y)=94 \\ x+2y=47 \end{gathered}`

put the vaue of x:

`\begin{gathered} x+2y=47 \\ 38-y+2y=47 \\ y=47-38 \\ y=9 \end{gathered}`

so there is 9 pigs and ducks is:

`\begin{gathered} x=38-y \\ x=38-9 \\ x=29 \end{gathered}`

The ducks is 29.