Question

grandpa has some cows and ducks in his farm. all in all there are 8 heads and 26 legs, how many cows and ducks are in there? solve this using factoring, finding multiples and divisibility rules

Answer 1

5 cows and 3 ducks

okay well there are 8 heads and each animal has a head meaning that there are a total of 8 organisms in total. Cows have 4 legs and ducks have 2. Lets say that c is cows and d is ducks. You would have the equations ...

c+d=8

4c+2d=26

well d techniacally = 8-c, so plug in (8-c) for the value of d

4c+2(8-c)=26. Distribute to get

4c+16-2c

and then add like terms. Soy ou would get

2c+16=26.

then just isolate the variable but subtracting 16 from both sides and dividing 2 on both sides. The answer you would get is that c=5 so there are 5 cows. Plug in 5 for c so you get 5+d=8 and tadaaaa you subtract 5 from both sides to get that there are 3 ducks.

hope this helps :)