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

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).

eudora eudora · Answer 2 · 2022-02-17T16:57:14+01:00

System of inequalities will be 2c + 4s ≥ 30 and c + s < 12

Graphing inequalities

Let the number of chickens = c

And the number of sheep = s

Known data,

Number of legs of one chicken = 2

Number of legs of one sheep = 4

Inequalities for the statements given,

"There were at least 30 legs"

2c + 4s ≥ 30 --------(1)

"There were fewer than 12 heads"

c + s < 12 --------(2)

Graph for the 1st inequality will be a dark line and area above the line will be the solution area (As shown in the graph attached).

Similarly, graph for the 2nd inequality will be a dotted line and area below the line will be the solution area (As shown in the graph attached).

Therefore, system of inequalities will be 2c + 4s ≥ 30 and c + s < 12.

Learn more about the system of inequalities here,

https://brainly.com/question/13066030?referrer=searchResults