How Many Pages in the Book? Solving a Problem with Fractions

Mathematical problems involving fractions can sometimes seem complex, but with a systematic approach, they can be easily solved. We will explore a problem involving fractions and solve it step by step. This problem can be useful for students practicing their skills or anyone looking to improve their problem-solving abilities.

The Problem

Liza has read 4/5 of the total number of pages of a book. Today she reads 21 pages. She still needs to read 1/10 of the total number of pages to finish reading the book. The challenge is to determine how many pages the book has in total.

Step-by-Step Solution

Step 1: Understand the Given Information

Liza has read 4/5 of the book. Loading remaining: Liza still needs to read 1/10 of the book. Today Liza reads 21 pages.

Let's denote the total number of pages in the book as x.

The total pages can be represented as:

x (4/5)x 21 (1/10)x

Step 2: Simplify the Equation

The first step is to combine the fractions:

(4/5)x (1/10)x 21 x

First, find a common denominator, which is 10:

(8/10)x (1/10)x 21 x

Combine the fractions and simplify:

(9/10)x 21 x

Move the (9/10)x term to the other side:

21 x - (9/10)x

Simplify the right-hand side:

21 (1/10)x

Step 3: Solve for x

Multiply both sides of the equation by 10 to solve for x:

x 210

Thus, the total number of pages in the book is 210 pages.

Verification

Pages read so far: 4/5 of 210 168 Pages to be read: 1/10 of 210 21

Loading total: 168 21 189

Judging from the information, after reading 21 pages today, Liza indeed finishes the book:

189 21 210

The calculations confirm the total number of pages is accurate.

Alternative Problem

Another similar problem is provided for practice:

A girl read 1/3 of the book on Monday, and 2/5 of the book on Tuesday. After these readings, there are 4/15 of the book remaining, and she still has 20 pages to read. How many pages are in the book?

Solution Steps

Step 1: Represent the remaining part

The remaining part of the book is 4/15, so:

4/15 of the book 20 pages

Thus, 1/15 of the book is 5 pages:

(1/15)x 5

Step 2: Calculate the total pages

15 x 5 75 pages

Hence, the total number of pages in the book is 75.

Conclusion

Through the step-by-step process, we can see that mathematical problems involving fractions and algebra can be resolved methodically. Whether Liza's 210-page book or the 75-page book, these solutions demonstrate how to apply fractions and algebraic equations to real-world problems. Practice and understanding the basics are key to mastering these skills.