Question

:

CHCK Farms raises hens and roosters. They have enough space to raise at most 300
300

birds per year. Each hen eats 80

80

pounds of food per year, and each rooster eats 60
60

pounds of food per year. The business can only afford 20,000

20
,
000

pounds of food per year. The graph below shows the solution set of a system of linear inequalities that represents this situation.

Answer 1

The number of hens is 100 and the number of roosters is 200.

Explanation:

Let the number of hens be x and the number of roosters be y

then the total number of hens and roosters, is 300

so,

`x+y \leq 300`----------------------------(1)

Also the hen eats 80 pounds of food per year and roosters eats 60 pounds of food per year,

`80x+60y \leq 20000`----------------(2)

To solve the equations , multilpy eq(1) by 80

`80x +80y \leq 24000`------------------(3)

Subracting (2) from (3)

`20y \leq 4000`

`y \leq 200`

substituting y in eq(1) we get

`x+200 \leq300`

`x \leq300 - 200`

x = 100