(NEED ASAP!!!) Algebra Word Problem

Question

You buy a new house and want to plant some trees for shade in the front yard. You plan on spending no more than $720 on the project. The large trees you want to plant cost $120 each and the smaller trees cost $80 each.

1) Write an inequality that represents the situation. Make sure you define your variables.

2) How would you graph the inequality on a coordinate grid that represents this situation?

3) What is the greatest number of small trees that you can purchase?

4) If you decided at the last minute you wanted to spend $40 on one rose bush as well, how does that change the amount of large and smaller trees you can buy?  

Answer 1

Hello! If your maximum budget is $720, then the inequality you set up has to reflect that the total money you spend is less than $720. So the next question is what is variable in this situation? Well, you can buy a number of large trees, and a number of small trees. If you call the number of large trees x, and the number of small trees y, you can do the following:

1. For your inequality, you need to convert the number of trees and the cost of one tree into the cost for all trees. Cost for all trees is number of trees × cost of one tree.
2. How do you graph an inequality that has two variables? I would suggest letting one variable be the variable on the y axis, and the other the variable on the x axis. Then try solving for the y axis variable. You will get something that looks like y ≤ mx + b. Do you know how to graph y = mx + b? If you do, then you can just graph that and color in all the areas below or above the line depending on if the inequality is ≤, or ≥ respectively.
3. How do you get the greatest number of small trees? Well, it would be how many small trees you can buy if you buy no large trees.
4. If you buy one $40 rose bush, then how much money do you have left to spend if you started with $720?

I hope this sets you on the right path! If you have further questions feel free to reach out.

Answer 2

x represents the number of large trees

y represents the number of small trees

120x + 80y ≤ 720

80y ≤ -120x + 720

y ≤ -1.5x + 9

Any pair of integer numbers shall satisfy.