Solving for the New Student's Marks: A Detailed Analysis for SEO

When dealing with problems that involve averages and ratios, it's crucial to break down the steps carefully and systematically. In this article, we'll explore a specific scenario—determining the marks of a new student in a class—using a step-by-step approach. This problem is a common type faced by students and educators, and understanding the process can be highly beneficial for optimizing search engine results pages (SERPs).

Scenario Overview

The problem at hand is as follows: in a class of 20 students, the average marks are 65. After adding a new student, the average marks increase by 2 points. The objective is to determine the marks of the new student.

Context and Importance for SEO

Understanding such mathematical problems can be useful for optimizing content for SEO. By breaking down complex problems into simpler steps, we can create more detailed and comprehensive articles that cater to a broader audience. Such content is often favored by search engines, leading to increased visibility and engagement.

Step-by-Step Breakdown

Given Information

No. of students 20 Average marks 65

Calculating Total Marks Before New Student

First, we need to calculate the total marks of the 20 students.

[text{Total marks} text{Number of students} times text{Average marks} 20 times 65 1300]

After Adding the New Student

With the addition of a new student, the total number of students becomes 21. We need to find the new average marks, which is 67 (65 2).

Calculating the New Total Marks

The new total marks can be expressed as:

[text{New total marks} text{New average marks} times text{New number of students} 67 times 21]

Solving for the New Student's Marks

Let's denote the marks of the new student as (x). The equation for the total marks after adding the new student is:

[text{New total marks} 1300 x]

Setting Up the Equation

[text{New total marks} 67 times 21 1300 x]

Now, we can solve for (x).

Solving the Equation

[text{1300} x text{1300} 67 times 21 - 1300] [text{1300} x text{1300} 1407 - 1300] [text{1300} x text{1407}] [text{x} text{1407} - text{1300}] [text{x} 107]

Conclusion

The marks of the new student are 107. This problem demonstrates the importance of understanding ratios and averages in a practical context. By solving such problems methodically, you can build a strong foundation in mathematics, which is essential for academic success and, in the long run, for optimizing content for Google and other search engines.

Key Takeaways for SEO

A clear and logical breakdown of the problem is crucial for both students and search engines. Maintaining a logical flow of information helps in creating SEO-friendly content. Use of relevant keywords in subheadings and throughout the content enhances visibility.

Keywords for SEO

The keywords used in this article include average marks, ratio increase, and new student's marks. These keywords help in making the content more discoverable for users searching for similar problems or methods.

Frequently Asked Questions (FAQs)

Q1: What is the total marks of 20 students, given the average is 65?

A1: The total marks of 20 students, given the average is 65, is 1300 (20 x 65).

Q2: What is the new average after adding a new student with marks of 107?

A2: The new average is 67, which is calculated as 65 2.

Q3: How does the addition of a new student affect the total marks?

A3: Adding a new student with marks of 107 increases the total marks from 1300 to 1407, resulting in a new average of 67.