Question

You are knitting a rectangular scarf. The pattern you have
created will result in a scarf that has a length of 60 inches and a width of
4 inches. However, you happen to have enough yarn to cover an area of
480 square inches. You decide to increase the dimensions of the scarf so
that all of your yarn will be used. If the increase in the length is 10 times
the increase in the width, what will the dimensions of the scarf be?

Answer 1

Let x = increase in the length and y = increase in the width

Answer 2

we are told that "the increase in the length is 10 times the increase in the width"

so

x = 10y

Answer 3

The original scarf looks like this

Answer 4

the new scarf (when the dimensions are increased) looks like this

Answer 5

basically you're adding on x and y to the corresponding dimensions (because our definitions allow us to do this)

Answer 6

Area

A = length * width

A = LW

A = (60+x)(4+y)

A = (60+10y)(4+y) .. plug in x = 10y

480 = (60+10y)(4+y) .. plug in A = 480 (this is the total area we want to use up all the yarn)

Answer 7

so your goal is to solve

480 = (60+10y)(4+y)

for y, then use that solution to find x