Question

A small farm has ducks and goats. There are 11 animals in all and 34 legs in all (wings don't count!). How many goats does the farm have? How many ducks?

Answer 1

5 ducks, 6 goats

Explanation:

We have some Goats and some Ducks. There are eleven animals in all:

`G+D=11`

Goats have 4 legs and Ducks 2. There are 34 legs altogether:

`4G+2D=34`

I'm going solve the first equation for `G` in terms of `D`, then substitute in:

`G=11-D`

`4(11-D)+2D=34`

and now solve for `D`:

`44-4D+2D=34`

`2D=10`

`color(blue)(ul(bar(abs(color(black)(D=5))))`

which will mean that `color(blue)(ul(bar(abs(color(black)(G=6))))`:

`G+D=11`

`G+5=11=>G=6`

And now let's check our leg count:

`4G+2D=34`

`4(6)+2(5)=34`

`24+10=34`

`34=34color(white)(000)color(green)sqrt`