Question

Luisa knit a rectangular scarf that measures 4 feet by 1 foot. She wants to use the remaining 6 square feet of fabric to create a border around the scarf.

How wide should the border of the blanket be?

Answer 1

Break it down. First, what are you being asked to find? The border of the blanket. So let's call that B. If the dimension of the scarf is 4' x 1', what will the dimension of the scarf with the border be (remember that a border goes all the way around). Draw a diagram. Once you have the diagram, come up with a formula for the area of the scarf with the border. Look at the diagram...you know the area of the scarf with the border and you know the area of the scarf without the border. What is the area of the border? How much fabric do you have for the border? Make that into an equation and solve it.

Answer 2

The area of the scarf I've already found which is 6, so with that info couldn't I do 6/4 to find what each side should be?

Answer 3

So 1.5 on each side of the border would take all 6 remaining feet of fabric.

Answer 4

(4 + 2x)(1 + 2x) - (4)(1) = 6 would be the equation to find the original area of the scarf without the border.

Answer 5

That's the formula for the area of the border to be 6, which is what you're being asked...nice job. Now solve it and you'll have the answer (remember that you're solving in feet).

Answer 6

So to answer my own question then you since your area of the scarf is 6 feet, and you have 6 more feet of fabric to work with and 4 sides it'd be 6/4 to get 1.5 feet on each side?

Answer 7

I'm sorry I missed the important factor that it's 6 feet squared, so it would be 2 feet on each side.

Answer 8

No. The formula in your previous post is for the area of the border, not the area of the scarf. (You're taking the area of the scarf with the border and subtracting the area of the scarf.) You want it to be equal to 6, the amount of fabric you have for the border. The formula is correct for the problem, now you just have to solve it for x.

Multiply everything out, move the 6 to the left side so you're solving for zero, refactor the quadratic, and solve. You'll end up with a negative solution and a positive solution. The positive solution is your answer. (Hint: It's between 0 and 1.)

Answer 9

Okay so I did it(I work fast and this is a multiple choice question which helps me.) and I came out with .5 feet, or 6 inches. I don't know if the multiple questions is what's screwing with me or what but I can't seem to find this, and Algebra confuses me so I don't know if I'm setting it up right either because I have problems with trinomials.

Answer 10

Sorry to take so long to respond back. If the border is supposed to go all the way around the scarf then .5 feet is the correct answer. If the border is only supposed to go on the sides of the scarf then .75 feet is the correct answer. If .5 is not one of the multiple choice answers and .75 is, then that's probably why.

Answer 11

.5 was actually put down as 6 inches and that was indeed correct, thank you.

Answer 12

You're welcome!