josie knits a scarf

Question

Josie knit a rectangular scarf that measures 6 feet by 1 foot. She wants to use

the remaining 4 square feet of fabric to create a border around the scarf. 

Write an equation Josie can use to find the required width of the border, x

Answer 1

First, draw a picture. The scarf is a rectangle with a length of 6 ft and a width of 1 ft. Wants to create a border of even width all the way around. Let's call the width of the border "x."

The area of the border is 4 square ft. (That's how much fabric she has left to use).

So the total area (including the border) minus the area of the main part of the scarf equals the area of the border.

(Note: * means "times")

The total area = (x + 6 + x) * (x + 1 + x). Simplifying this we get: (6 + 2x)(1 + 2x)

The area of the main part of the scarf: 6 * 1 = 6

The area of the border = 4

So, put it together:

(6 + 2x)(1 + 2x) - 6 = 4

Simplify

(6 + 2x)(1 + 2x) = 10

Not sure if they need you to go any further, since the question only asked you to write an equation, not solve it.