Question

A farmer owns chickens and sheep. One day, he observed that when his animals were all together, there were at least 30 legs but fewer
than 12 heads. (All of the animals have the expected number of heads and legs.) Let c be the number of chickens and s be the number of
sheep. State a system of inequalities that models this problem and graph it.
c+s 5 12 and 2c + 45 2 30

Answer 1

Answer:

c+s < 12, 2c+4s >= 30.

Step-by-step explanation:

Known: at least 30 legs, less than 12 heads.

Each animal has one head, so if there are less than 12 heads, then c + s < 12.

Sheep have four legs and chickens have two legs, so if there are at least 30 legs, then # of chicken legs + # of sheep legs >= 30, ----> c(2) + s(4) >= 30, ----> 2c + 4s >= 30.

The graph attached models the problem is you set the x axis as "c" (# of chickens) and y axis as "s" (# of sheep).