Question

The number of ducks and pigs in a field totals 46. The total number of legs among them is 126. 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

The number of ducks is 29 and the number of pigs is 17

Step-by-step explanation

Suppose, the number of ducks
`=d` and the number of pigs
`=p`

As the total number of ducks and pigs in the field is 46, so the first equation will be......

`d+p=46...........................................(1)`

Now, each duck has exactly two legs and each pig has exactly four legs. The total legs in the field is 126. So, the second equation will be.....

`2d+4p = 126......................................(2)`

Solving equation (1) for getting 'd' itself ......

`d= 46-p`

Now, we will substitute this
`d= 46-p` into equation (2). So we will get.....

`2(46-p)+4p=126\\ \\ 92-2p+4p=126\\ \\ 2p= 126-92\\ \\ 2p= 34\\ \\ p=(34)/(2)=17`

Plugging this
`p=17` into equation (1), we will get...

`d+17=46\\ \\ d=46-17=29`

So, the number of ducks is 29 and the number of pigs is 17