Systems of Inequalities question

Question

Amy is a landscaper and has been given an assignment to modify the plans for a park in a small neighbourhood. The land she is working on is covered in trees and shrubs.

Amy needs to make the park smaller by adding a fence.

Part 1 - She must first calculate how many trees and how many shrubs she can keep in the park,

• There must be a total of 20 plants

• Each shrub requires 3 L of fertilizer and each tree requires 0.5 L of fertilizer. Amy has 22.5L of fertilizer.

Let x = number of trees Let y = number of shrubs

Solve for the number of trees and shrubs: "I found x = 15 and y = 5" I am having trouble solving Part 2 :

The park is represented by the shaded area and is bordered by a road, given by the inequality y ≤ 3/2 x + 8.

Amy must make the park smaller by adding a fence, and the fence must be perpendicular to the road. (The y-intercept of the fence must be different then the y-intercept of the road)

Part 2 – On the Cartesian plane graph the fence and shade that area that coresponds to the new park containing the correct number of trees and shrubs calculated in part 1 ( i will graph it it i just don't know how to find the inequality)

Part3: Give the inequality that represents the fenced in park area you have drawn on the Plane.

What is the inequality for the fence and shaded area that corresponds to the new park area containing the correct number of trees and shrubs calculated in Part 1.

Answer 1

Hints:

• Perpendicular lines have slopes that are negative reciprocals of each other.
• There are (infinitely) many possible $y$-intercepts you can use for the fence. By inspection, $2$ should work.
• An inequality of the form $y \leq mx + b$ means that you shade below the line, while an inequality of the form $y \leq mx + b$ means that you shade above the line.