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?

1 Answer

Answer:

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#