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 typoe of cord and y represents the lend of the second type of cord, shade the region of the coordinate plan that repsents the lengs of each type of cord she could purchase. State the inequalities that define this region.

I don't know if I'm even supposed to do this but I'm trying to solve it out first,
x=length of cord #1
y=length of cord #2
x=1.5g per metre
y=2.00g per metre

So x+y <=6.0g

And I don't know where to go from there.
Thank you.

The inequality you want to solve is 1.5x + 2y <= 6. Graph the edge, which is the line 1.5x + 2y = 6. (This line has a slope of -3/4, x-intercept at (4 , 0) and y-intercept at (0 , 3)). Use the origin (0 , 0) as a test point. Since 1.5(0) + 2(0) = 0 and that is <= 6, shade the half-plane where the origin is located. However, limite your solution region to the 1st quadrant, since in the context of this problem, x and y are both non-negative (you're not going to purchase a negative number of yards of cord.)

That makes sense now. Thank you.

You're welcome. Glad to help.