Math Problem Statement

On the first day of vacation, you read one-quarter of a novel. On the second day, you read half of the remaining pages. On the third day, you read the last 135 pages of the novel.How many pages does the novel have?

Solution

Let's denote the total number of pages in the novel as xx.

Step 1: First Day

  • On the first day, you read one-quarter of the novel: Pages read on the first day=14x\text{Pages read on the first day} = \frac{1}{4}x
    • Remaining pages after the first day: Remaining pages=x14x=34x\text{Remaining pages} = x - \frac{1}{4}x = \frac{3}{4}x

Step 2: Second Day

  • On the second day, you read half of the remaining pages: Pages read on the second day=12×34x=38x\text{Pages read on the second day} = \frac{1}{2} \times \frac{3}{4}x = \frac{3}{8}x
    • Remaining pages after the second day: Remaining pages=34x38x=38x\text{Remaining pages} = \frac{3}{4}x - \frac{3}{8}x = \frac{3}{8}x

Step 3: Third Day

  • On the third day, you read the remaining pages, which is 135 pages: 38x=135\frac{3}{8}x = 135

Step 4: Solve for xx

  • To find the total number of pages xx, solve the equation: x=135×83=360x = \frac{135 \times 8}{3} = 360

So, the novel has 360 pages.

Would you like more details, or do you have any questions?

Here are 5 related questions to expand your understanding:

  1. How many pages did you read on the first day?
  2. How many pages did you read on the second day?
  3. What fraction of the novel was read by the end of the second day?
  4. How many pages would be left if the novel had 450 pages and you followed the same reading pattern?
  5. How would the solution change if you read one-third of the remaining pages on the second day instead?

Tip: When solving problems involving fractions of a whole, breaking down each step clearly helps in keeping track of what remains and ensures accurate calculations.