1. ## Inequality check.

Hey folks, I got a problem here and I think that I have a solution, but the wording of the question makes me think I'm short on the problem.

Alice has gone to the hardware store to purchase two different kinds of cord she uses in kite construction. The first type of cord has a mass of $1.50g$ per metre, and the second type has a mass of $2.00g$ per metre. she intends to purchase no more than $6.0g$ in total. If $x$ represents the length of the first type of cord and $y$ represents the length of the second type of cord, shade the region in the coordinate plane that represents the lengths of each type of cord she could purchase. State the inequalities that define this region.
So I started with the inequality I found and manipulated it into a staight line inequality from there. We know that $y$ must be less than or equal to because she wants no more than $6$, right?

So here's what I did.

$1.5x+2y \leq 6$

$2y \leq 6 - 1.5x$

$y \leq -\frac{3}{4}x+3$

So I want to just graph this line and shade underneath it, but is there another inequality I'm missing? The question says "State the inequalities that define this region."

Thanks!

2. You have : $x\geq 0 , y\geq 0$ because they must be positive.

But i'm not sure about the inequality because the condition stated is about mass, whereas x and y are length....i don't know how to do this myself...sorry^^

3. My thinking is that they want $0\leq y \leq -\frac{3}{4}x +3;$ i.e., she needs to buy something?

Should probably get a second opinion, though, because the wording of word problems always trips me up much more than the math.

4. Originally Posted by AlephZero
My thinking is that they want $0\leq y \leq -\frac{3}{4}x +3;$ i.e., she needs to buy something?

Should probably get a second opinion, though, because the wording of word problems always trips me up much more than the math.
You have it right. If you simply graph the linear equation and shade underneath the line, the problem doesn't make sense as it applies to reality. Shading the region bounded by y=0, x=0 and the line y=(-3/4)x+3 will give you the region that corresponds to the problem. However, from the question it looks like she has to buy SOMETHING of each of the chord types so your axis lines should be dashed indicating they are not included in the solution.

5. I think it's not dashed. It's possible if x = 0 because it will give a certain value of y

6. Originally Posted by songoku
I think it's not dashed. It's possible if x = 0 because it will give a certain value of y
Certainly. However that would suggest she only uses one type of chord. Which is valid, but doesn't seem to fit the parameters of the question.

7. Originally Posted by ANDS!
Certainly. However that would suggest she only uses one type of chord. Which is valid, but doesn't seem to fit the parameters of the question.
Craigston's first post is correct.

And yes, it does state that she intends to buy two different cords, but let's be realistic; if you can include a length of cord $x=0.0000000000000001$, you can include 0. Your teacher will not mark you down for this.

Remember, when thinking about what a feasable domain of a function could be, look at all of the possibilities. In other words, it is "feasable" that the lady gets to the store and decides she wants to blow her wad on one cord.