Question

Julia has a farm on a rectangular piece of land that is 150150150 meters long. This area is divided into two parts: A square area where she lives (whose side is the same as the width of the farm), and the remaining area where she grows artichokes.
Every week, Julia spends \$8$8dollar sign, 8 per square meter on the area where she lives, and earns \$4$4dollar sign, 4 per square meter from the area where she grows artichokes. This way, she manages to save some money every week.

Write an inequality that models the situation. Use w to represent the width of Julia's farm.

Answer 1

the instructions aren't super clear to me but I'll give it my best shot



the length of the land is 150 m, with unknown width w
the square area where she lives has the same width as the artichoke plot, and therefore is w^2

the width of the artichoke plot is w, while the length is 150-w (since the entire plot is 150 m long and the living area is w units wide)

so the artichoke area is (150-w)(w)

from there, we know that she spends 8 dollars per square meter on the living space, so the amount spent is simply 8*w^2

same logic with the artichoke (4 dollars per square meter)

since it says she's saving money, that means she's earning more from the garden than she's spending, so set amount earned > amount spent and re-arrange for w as needed