Solving the George and the Book Problem: A Comprehensive Guide Using Algebra

Introduction

The problem presented involves a reader, George, who is reading a book but has specific reading patterns on different days. We need to determine the total number of pages in the book and how many pages George has left to read. This problem can be effectively solved using algebraic equations.

Understanding the Problem

Let's denote the total number of pages George needs to read as x. Here’s a breakdown of the reading pattern:

On Monday, George reads frac{1}{3}x of the book. On Tuesday, he reads frac{3}{10} of the remaining pages, which is based on the remaining pages after Monday's reading. After Tuesday, George has 35 pages left to read.

Mathematical Representation and Solution

To solve the problem, we can set up the following equations:

Pages read on Monday: George reads frac{1}{3}x Remaining pages after Monday: frac{2}{3}x Pages read on Tuesday: frac{3}{10} cdot frac{2}{3}x frac{1}{5}x Remaining pages after Tuesday: frac{2}{3}x - frac{1}{5}x frac{7}{15}x The problem states that after Tuesday, George has 35 pages left to read: frac{7}{15}x 35

Step-by-Step Solution

To find the total number of pages in the book, we solve the equation:

frac{7}{15}x 35

Multiplying both sides by frac{15}{7}:

x 35 cdot frac{15}{7} 75 pages

Therefore, the total number of pages in the book is 75. Let's verify:

Pages read on Monday: frac{1}{3} cdot 75 25 pages Pages remaining after Monday: 75 - 25 50 pages Pages read on Tuesday: frac{3}{10} cdot 50 15 pages Pages remaining after Tuesday: 50 - 15 35 pages

Conclusion

The book has 75 pages, and George has 35 pages left to read. This problem showcases the application of algebraic equations in solving real-world problems.