SOLUTION: I'm doing a project to solve "You and your classmates decide to sell sweatshirts and T-shirts to raise money for a school trip. You decide that you should sell at least thirty item

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Question 727196: I'm doing a project to solve "You and your classmates decide to sell sweatshirts and T-shirts to raise money for a school trip. You decide that you should sell at least thirty items, but do not want to exceed 120 items. Based on a small survey of students, you also decide that the number of T-shirts should be at least twice the number of sweatshirts." I usually have no problem, but I'm struggling. First I need to make 3 inequalities, I tried "x+y≥30 ; x+y≤120 ; x≥2y" We need to graph and shade to form a polygon. These inequalities did not work.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
If x = # of sweatshirts sold and y = # of T-shirts sold then the three inequalities should be

x+y ≥ 30
x+y ≤ 120
y ≥ 2x
Then you must add on x ≥ 0 and y ≥ 0 to make sure that you don't sell a negative number of either.

So in total, you'll have these 5 inequalities
x+y ≥ 30
x+y ≤ 120
y ≥ 2x
x ≥ 0
y ≥ 0

Now you graph each inequality (let me know if you need help doing this) and shade the appropriate region. The final solution set region will be the region where ALL of the inequalities overlap. This region is shown below

Note: the pieces of the blue lines that are not touching the red shaded region are not part of the solution set, they are just part of the boundary lines

If you were to erase all of the parts of the lines that aren't in the solution region, then you would get something like this

That graph above is a better picture of the red solution region and the solid blue lines that make up the border of the solution region are also part of the solution set.

Basically if a point lies in that region or on the boundary, then it's a solution to all 5 inequalities that make up the system.