Question

Kona wants to bake at most 30 loaves of banana bread and nut bread for a bake sale. Each loaf of banana bread sells for $2.50, and each loaf of nut bread sells for $2.75. Kona wants to make at least $44. Which system of inequalities models the situation?

1) x + y < 30, 2.5x + 2.75y < 44
2) x + y ≤ 30, 2.5x + 2.75y ≥ 44
3) x + y > 30, 2.5x + 2.75y > 44
4) x + y ≥ 30, 2.5x + 2.75y ≥ 44

Answer 1

The system of inequalities that models Kona's situation of baking at most 30 loaves of bread to make at least $44 is represented by x + y ≤ 30 and 2.5x + 2.75y ≥ 44.

Step-by-step explanation:

Kona wants to bake at most 30 loaves of bread for a bake sale and aims to make at least $44 from selling banana and nut bread.

Let x represent the number of loaves of banana bread and y represent the number of loaves of nut bread.

To model Kona's situation, we need a system of inequalities that satisfies both conditions: the total number of loaves and the total revenue.

The first condition that Kona wants to bake at most 30 loaves leads to the inequality x + y ≤ 30. This means that the sum of banana and nut bread loaves should not exceed 30.

The second condition is that Kona wants to make at least $44 from the sales, which corresponds to the inequality 2.5x + 2.75y ≥ 44 where 2.5 and 2.75 are the prices for each loaf of banana bread and nut bread, respectively.

Combining these inequalities, the appropriate system that models the situation is option 2: x + y ≤ 30, 2.5x + 2.75y ≥ 44.