Question

A gardner will use up to 230 square feet for planting flowers and vegetables. He wants the area used for vegetables to be at least 3 times the area used for flowers. let x be the area in square feet used for flower. let y denote the area in square feet used for vegetables.

Answer 1

The question involves inequalities and area calculations for a garden.

Step-by-step explanation:

The student's question relates to mathematical inequalities and area calculations within a given parameter. According to the problem, the gardener has a maximum of 230 square feet for planting. If x represents the area for flowers and y represents the area for vegetables, the inequality y ≥ 3x defines the relationship between the two areas, where the gardener wants the vegetable area to be at least three times the flower area.

Additionally, combined they must not exceed 230 square feet, resulting in the inequality x + y ≤ 230.

By substituting the first inequality into the second, it becomes x + 3x ≤ 230, simplifying to 4x ≤ 230. Dividing both sides by 4, we have x ≤ 57.5, meaning the maximum area for flowers is 57.5 square feet. For the vegetable area, we substitute x into the first inequality, y ≥ 3(57.5), giving us y ≥ 172.5 square feet for the vegetable area. These inequalities fulfill the conditions set by the gardener for his planting areas.