Question

larry wants to buy some carpeting for his living room. The length of the room is 2 times the width and the total area of the room is 18 square meters. What is the length of the living room?

Answer 1

They want you to turn the word problem into a set of equations - you will need two equations since you have two unknowns (the length and width of the living room).

Answer 2

The first equation relates length to width:
1. l = 2w (the length is twice the width)
The second equation tells you the area, which we know is l*w for any rectangle.
2. lw = 18

Answer 3

Do you know how to solve it from there?

Answer 4

One way is to "substitute" the first equation into the second equation. So since the first equation says that l = 2w, we replace "l" in the second equation with "2w":
3. 2w*w = 18
4. 2w^2 = 18
5. w^2 = 18/2
6. w^2 = 9
7 w = sqrt(9)
8. w = 3.
So now you know the width of the room is "3" meters.
Now substitute that back into either of the first two equations and solve for l, the length.

Answer 5

1. l = 2w
2. l = 2*3
3. l = 6
The length of the room is 6

Answer 6

I'll leave it to you to check the work - given l = 6 and w = 3, does the word problem make sense when you plug in those values (do both equations work?).

Answer 7

Let me know if you're confused.