Question

problem 3
write an equation for each line.
graph omitted
problem 4
a publisher wants to figure out how thick their new book will be. the book has a front cover and a back cover, each of which have a thickness of \\(\frac{1}{4}\\) of an inch. they have a choice of which type of paper to print the book on.

a. bond paper has a thickness of \\(\frac{1}{4}\\) inch per one hundred pages. write an equation for the width of the book, \\(y\\), if it has \\(x\\) hundred pages, printed on bond paper.

b. ledger paper has a thickness of \\(\frac{2}{5}\\) inch per one hundred pages. write an equation for the width of the book, \\(y\\), if it has \\(x\\) hundred pages, printed on ledger paper.

c. if they instead chose front and back covers of thickness \\(\frac{1}{3}\\) of an inch, how would this change the equations in the previous two parts?

Explanation:

Problem 3

Step1: Identify horizontal lines

Horizontal lines have the form $y = k$, where $k$ is the y-intercept.

• Top brown line: $y = 5$
• Middle black line: $y = 0$
• Bottom blue line: $y = -2$

Step2: Identify vertical lines

Vertical lines have the form $x = k$, where $k$ is the x-intercept.

• Green line: $x = 0$
• Orange line: $x = 6$

Part a

Step1: Total cover thickness

Each cover is $\frac{1}{4}$ inch, so total cover thickness: $\frac{1}{4} + \frac{1}{4} = \frac{1}{2}$ inch

Step2: Paper thickness term

Bond paper is $\frac{1}{4}$ inch per 100 pages, so for $x$ hundred pages: $\frac{1}{4}x$

Step3: Combine for total thickness

Total book width $y = \text{paper thickness} + \text{cover thickness}$
$y = \frac{1}{4}x + \frac{1}{2}$

Part b

Step1: Total cover thickness (same as a)

Total cover thickness: $\frac{1}{2}$ inch

Step2: Paper thickness term

Ledger paper is $\frac{2}{5}$ inch per 100 pages, so for $x$ hundred pages: $\frac{2}{5}x$

Step3: Combine for total thickness

$y = \text{paper thickness} + \text{cover thickness}$
$y = \frac{2}{5}x + \frac{1}{2}$

Part c

Step1: New total cover thickness

Each new cover is $\frac{1}{3}$ inch, so total cover thickness: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$ inch

Step2: Update equations

Replace the constant term $\frac{1}{2}$ with $\frac{2}{3}$ in both equations.

Answer:

Brown line: $y = 5$
Black line: $y = 0$
Blue line: $y = -2$
Green line: $x = 0$
Orange line: $x = 6$

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Problem 4