Question

A barn has 11 heads and 36 legs. How many are chicks and how many are pigs

Answer 1

c = amount of chickens

p = amount of pigs

now, let's recall that chicken have two legs, and pigs have four legs, whatever "c" is, the amount of legs for all chicken is 2*c, or 2c.

the amount of legs for pigs is 4*p or 4p.

we know there are 36 legs total, therefore 2c + 4p = 36.

we also know that there are 11 heads, since each only has one head, then c + p = 11.

`\bf \begin{cases} 2c+4p=36\\ c+p=11\implies \boxed{p}=11-c \end{cases}~\hspace{5em}\stackrel{\textit{using \boxed{p} in the first equation}}{2c+4\left( \boxed{11-c} \right)=36} \\\\\\ 2c+44-4c=36\implies -2c=-8\implies c=\cfrac{-8}{-2}\implies \blacktriangleright c=4 \blacktriangleleft \\\\\\ \stackrel{p=11-c}{p=11-4}\implies \blacktriangleright p=7 \blacktriangleleft`

Answer 2

answer is 7 pigs and 4 chicks

pigs' legs = 7 x 4 = 28

chicks' legs = 4 x 2 = 8

28 + 8 = 36 legs