Question

Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this section to solve the following exercise.The number of ducks and pigs in a field totals 37. The total number of legs among them is 98. Assuming each duck has exactly two legs and each plg has exactly fourlegs, determine how many ducks and how many pigs are in the field.ducks?pigs?

Answer 1

Lets call x to the number of ducks

and y the number of pigs.

Then:

`2x+4y=98`

Because there are 2 legs per duck and 4 legs per pig.

If the total of animals is 37, then:

`x+y=37`

Then:

`x=37-y`

And replacing on the first equation we get:

`2(37-y)+4y=98`
`74-2y+4y=98`
`2y=98-74`
`2y=24`
`y=(24)/(2)`
`y=12`

There are 12 pigs and therefore 25 ducks.