Question

To be considered a periodical under the post office's rules, a magazine must have no more than \(25 \%\) advertising content. The present issue of the magazine that Aram manages has 172 pages but is \(28.5 \%\) ads. How many pages must Aram convert from ads to nonadvertising content to meet the post office's requirement? A. 4 B. 5 C. 6 D. 7

Short answer

Aram must convert 7 pages to meet the requirement.

Step-by-step solution

- Calculate current number of ad pages

To find the number of pages devoted to advertising, multiply the total number of pages by the percentage of ad content: \[ 172 \times 0.285 = 49.02 \text{ pages} \]

- Calculate the maximum allowed ad pages

Calculate the maximum number of ad pages allowed by the post office's rule: \[ 172 \times 0.25 = 43 \text{ pages} \]

- Determine the pages to be converted

Subtract the maximum allowed ad pages from the current number of ad pages to find the pages that need to be converted: \[ 49.02 - 43 = 6.02 \text{ pages} \] Since pages must be whole numbers, round 6.02 up to 7.

Key concepts

percentages

Percentages are a way to express a number as a fraction of 100. They are widely used to compare values and find proportions. In everyday situations, we use percentages to express things like discounts, interest rates, and test scores.
For example, in the exercise about the magazine, the percentage of advertising content is given as 28.5%. This means 28.5 pages out of every 100 pages are ads.
To calculate the number of ad pages in the magazine, we multiply the total pages by the percentage in its decimal form:
Larger percentage values mean more ad content, so reducing the ad percentage ensures compliance with guidelines.

advertising content requirements

Understanding advertising content requirements involves knowing the rules that limit the amount of ad space in publications. In this exercise, the post office's rule states that no more than 25% of a magazine can be ads. This helps ensure that readers get more valuable content and not just advertisements.
To comply, we need to figure out how many pages are ads and how many need to be changed to non-ad content. By staying within the allowed percentage, the magazine can continue to qualify as a periodical.
For example, if a magazine has 172 pages, no more than 25% can be ads. That means a maximum of 43 pages can be ads. If our magazine currently exceeds this limit, we must reduce the ad content to meet the rules.

conversion calculations

Conversion calculations help us find out how much of one type of content we need to change to another type. In the magazine example, we need to convert ad pages to non-ad pages to meet the requirement.
First, calculate the current ad pages by multiplying the total pages by the ad percentage. Then, find the maximum allowed ad pages by multiplying the total pages by the allowed percentage.
Subtract the allowed ad pages from the current ad pages to determine how many pages must be converted. Here, our example shows:

• Ad Pages = 172 × 0.285 = 49.02 pages
• Allowed Ad Pages = 172 × 0.25 = 43 pages

Finally, convert the necessary pages to comply with the rules.

whole number rounding

Whole number rounding simplifies numbers to make them easier to work with. In conversions or calculations, it helps to meet practical constraints. For example, you can’t have part of a page in a magazine, so you need to round to whole pages.
In this exercise, subtracting the allowed ad pages from the current ad pages gives us the number 6.02. Since you can't have 0.02 of a page, rounding 6.02 up to the next whole number, 7, ensures compliance.
Rounding usually follows these rules:

• If the decimal is 0.5 or higher, round up.
• If it's less than 0.5, round down.

This way, calculations align with real-world applications, keeping the results practical and accurate.