Question

martha believes her printer is out to get her. most days it behaves well, but every time she has a big report due, it mangles one out of every eight pages.

1. if the report was sixteen pages long, how many pages did the printer mangle?
2. if marthas whole report was seventy - two pages long, how many of the pages did the printer mangle?
3. heres the truth. the printer mangled only one page of the report. how long was the whole thing?

enter a variable for the number of pages in the whole report and use this variable to write an expression for the number of pages mangled.
after completing the worksheet, graph your model.

Explanation:

Step1: Identify the ratio

The printer mangles 1 out of every 8 pages. So the ratio of mangled - to - total pages is $\frac{1}{8}$.

Step2: Solve Question 1

For a 16 - page report, let $n$ be the number of mangled pages. We use the proportion $\frac{n}{16}=\frac{1}{8}$. Cross - multiply: $8n = 16$, then $n=\frac{16}{8}=2$.

Step3: Solve Question 2

For a 72 - page report, let $m$ be the number of mangled pages. Using the proportion $\frac{m}{72}=\frac{1}{8}$. Cross - multiply: $8m = 72$, then $m=\frac{72}{8}=9$.

Step4: Solve Question 3

Let $x$ be the number of pages in the whole report. Since the ratio of mangled to total pages is $\frac{1}{8}$ and the number of mangled pages is 1, we have the equation $\frac{1}{x}=\frac{1}{8}$. Cross - multiply to get $x = 8$.

Answer:

Question 1: 2
Question 2: 9
Question 3: 8