Problem 109 - Prealgebra

Question

In the U.S. Patent and Trademark Office, 6000 examiners have a backlog of 770,000 new, unexamined applications for patents. How many applications is that for each examiner to catch up on? Round your answer to the nearest tenth. Associated Press-Times-Standard 5/5/09

Step-by-Step Solution

Answer

128.3 applications per examiner.

Step 1: Understanding the Problem

We need to find out how many patent applications each examiner needs to handle to clear the backlog. We have 770,000 applications and 6,000 examiners.

Step 2: Setting Up the Division

The total number of applications is 770,000, and the total number of examiners is 6,000. To find the number of applications per examiner, divide the total applications by the number of examiners.

Step 3: Perform the Division

Calculate \[\frac{770,000}{6,000} = 128.3333...\] This calculation tells us the average number of applications per examiner.

Step 4: Rounding the Result

Since the question asks for the result to be rounded to the nearest tenth, we look at the first decimal place of 128.3333..., which is 3. Since it is less than 5, we round down, giving us 128.3.

Key Concepts

Backlog Calculation

In the context of a backlog calculation, it's important to understand what "backlog" means. A backlog can be described as a queue of tasks or items waiting to be completed or addressed. For the U.S. Patent and Trademark Office, the backlog is the large number of patent applications awaiting examination, which, in this case, is a total of 770,000 applications.

To determine the workload effectively, we need to distribute this backlog among the available workforce, which consists of 6,000 examiners. This involves dividing the total number of applications by the number of examiners to find out how many applications each examiner is responsible for. This calculation is crucial for effectively managing workload and ensuring timely processing. Hence, in this scenario, we perform the calculation:

• Total applications: 770,000
• Total examiners: 6,000
• Applications per examiner: \(\frac{770,000}{6,000}\)

This simple division gives us the average number of applications each examiner needs to process to clear the backlog.

Rounding Numbers

Rounding numbers is a mathematical technique used to simplify numbers, making them easier to deal with, especially when precise calculations are not necessary. When a result includes many decimal places, rounding helps present a more concise figure by eliminating less significant digits.

In our problem, the division yields 128.3333 applications per examiner. To meet the requirement for simplifying the answer, we need to round it to the nearest tenth. This means looking at the digit in the tenths place, which is 3 here.

• If the digit following the tenths digit is 5 or more, we round up.
• If it's less than 5, we round down.

In this scenario, since the number directly after the first digit is 3 (less than 5), we round down so that the average number of applications per examiner is 128.3. Understanding rounding rules like this helps in presenting manageable and practical numbers.

Average Applications per Examiner

Calculating the average applications per examiner is a specific case of finding the average in mathematics, which involves dividing a total by a count of items. This simple arithmetic calculation helps us understand how much work each examiner has on their desk.

Here's how it works:

• You start with the total number of items (770,000 applications).
• Divide this total by the number of units or groups (6,000 examiners).
• After performing this division, we get an average value representing the workload per examiner.

Such averages are essential in practical scenarios to evenly distribute tasks and ensure fair management. Therefore, understanding this concept helps organizations and individuals organize resources effectively.

The concept of averages is widely used beyond just workload distribution. An understanding of averages can apply to numerous fields, making it a versatile mathematical tool.