Chapter 8.5, Problem 9E

To determine

To find:

After how many will you finish the scarf?

Answer to Problem 9E

It will take 6 days to finish the scarf.

Explanation of Solution

Given:

You and a friend are knitting a scarf that will be 72 inches long. Your friend knits the first 24 inches and then given you the scarf to finish. You expect to knit at a rate of 8 inches per day.

Calculation:

Let y represent the length of scarf after x days of knitting.

We have been given that you will knit at a rate of 8 inches per day, so scarf knitted in x days would be $8x$ .

The total length of scarf knitted after x days would be $8x$ plus length knitted by your friend. We can represent this information in an equation as:

  $y=24+8x$

The slope of the line is 8 and the y -intercept is 24. Upon graphing our equation, we will get our required graph as shown below:

  

The solution of our given problem will be intersection of equation $y=24+8x$ and $y=72$ .

Upon looking at our given graph, we can see that after 6 days the value of y would be 72.

Therefore, it will take 6 days to finish the scarf.