The system of linear inequalities given in the problem is:

$4x + 5y \leq 180$ $x + y \geq 40$

We are tasked with determining which situation corresponds to this system.

• The inequality $4x + 5y \leq 180$ suggests that there is a constraint on the total value or weight of something, with 4 units of one item (represented by $x$) and 5 units of another item (represented by $y$). The total of these cannot exceed 180.

• The inequality $x + y \geq 40$ indicates that there is a minimum total quantity required, in this case, at least 40 units.

Analysis of the options:

• A. The bookstore example refers to selling at least 40 sets of notebooks, but the constraint is about sets of notebooks, not weight or anything resembling the coefficients 4 and 5. Also, there's no clear link to the 180 value.

• B. The grocery store example fits well because it mentions oranges sold in 4-pound and 5-pound bags. The store wants to limit the total weight of oranges to no more than 180 pounds, and they also want to sell at least 40 bags. This matches the constraints of the system: $4x + 5y \leq 180$ represents the weight limit, and $x + y \geq 40$ represents the minimum number of bags sold.

• C. The math test situation involves points per question, but it does not directly relate to the inequalities based on weight or a count of items. The numbers don't correspond to a maximum of 180 and minimum of 40 in the same meaningful way.

• D. The pharmacy example talks about revenue and prices, not weights or counts in the same form as the inequalities.

Conclusion:

The correct answer is B, which describes a grocery store selling oranges in 4-pound and 5-pound bags, limiting the total weight to 180 pounds and ensuring they sell at least 40 bags each day.

Would you like a detailed breakdown of how the inequalities were interpreted?

Here are 5 related questions you could explore:

1. How do we graph a system of inequalities like this one?
2. How would the solution change if the grocery store wanted to sell exactly 40 bags of oranges instead of "at least"?
3. How can we solve systems of linear inequalities algebraically?
4. What happens if the weight limit increases to 200 pounds? How does that affect the inequalities?
5. How could we set up similar inequalities for other real-world problems?

Tip: When solving word problems, pay close attention to how the coefficients in inequalities correspond to quantities or constraints like weight, price, or total units.