Question

Mr. Stanford wrote 65 pages of a travel brochure. He wants to divide it into 8 equal sections. How many pages will be in each section?

What is the answer as a mixed number?

Answer 1

Is this question correct? I get `8 1/8` pages

Explanation:

Treat as a ratio

65 pages for 8 equal sections.

Write the ratio in the format of a fraction.

`("65 pages")/("8 sections")`

But we need the number of pages for 1 section. So we need to change the 8 into 1.

For multiply or divide in ratios expressed as fractions what we do to the bottom we do to the top.

Divide top and bottom by 8 giving

`65/8-=(65-:8)/(8-:8) = 8.125/1`???????

Giving: each section will be `8 1/8` pages for each section
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Note that
`7xx8=56`
`8xx8=64`
`9xx8=72`

`color(red)("You will not obtain a whole number answer for 65 pages")`
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`color(blue)("Alternative solution")`

Suppose each section was to start on a new page

Then each section would end on the next 9th page with `7/8`ths of it blank. Giving a total number of pages as 8 sections at 9 pages each. Thus we have a total page count of `8xx9=72`

This is a lot more than the given count of 65????

Answer 2

NO one will produce a brochure of 65 pages - it is simply not practical nor cost-effective.

Explanation:

In practical terms, no one would produce a brochure of 65 pages. A page has two sides, but as brochures are printed in booklet format, there are always 4 "pages" to a sheet of paper. Therefore any brochure has to be a multiple of 4 to avoid wasting, No one would produce a brochure with 3 totally blank page.

The obvious answer is `65÷8 =`8 1/8#, but this is unlikely as explained above.

Also, even if there are only a few lines at the top of the last page, there will still be whole sheet of paper used.

The advice would be:
Condense the amount of some of the text to fit into `7 1/2` pages and use the left over space for a cover page and a list of contents, with some tempting photographs..