Word Problem : Book

Find the total number of pages in the book:
Marie has finished $\frac{3}{4}$ of a book. She found that she has read 106 more pages than the number of pages left to read. What is the total number of pages in the book?

Let $x$ be the total number of pages in the book.
Step 1: Define what we know
Marie finished $\frac{3}{4}$of the book, which means she has read $\frac{3}{4}x$pages.
She has $106$ more pages left to read, which means she has $x – \frac{3}{4}x = \frac{1}{4}x$ ​pages remaining.

According to the problem, the number of pages she has read is 106 more than the number of pages left to read. Therefore, we can write the equation:
$$\frac{3}{4}x = \frac{1}{4}x + 106$$

Step 2: Solve the equation
First, subtract $\frac{1}{4}x$from both sides:

$$\frac{3}{4}x – \frac{1}{4}x = 106$$

$$\Rightarrow \frac{2}{4}x = 106$$

$$\Rightarrow \frac{1}{2}x = 106$$
Now, multiply both sides by $2$:

Step 3: Verify the result
Total number of pages is $212$.
Pages read: $\frac{3}{4} * 212 = 159$
Pages left: $\frac{1}{4} * 212 = 53$
The difference: $159 – 53 =106$, which matches the given information.

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