After reading `(7)/(9)` of a book, `40` pages are left. How many pages are there in the book?

Options

A. `170`
B. `280`
C. `180`
D. `200`

Answer

To find the total number of pages in the book, we can follow these steps:

### Step 1: Define the total number of pages
Let the total number of pages in the book be \( x \).

### Step 2: Determine the pages read
According to the problem, \( \frac{7}{9} \) of the book has been read. Therefore, the number of pages read is:
\[ \text{Pages read} = \frac{7}{9} x \]

### Step 3: Determine the pages left
It is given that there are 40 pages left after reading \( \frac{7}{9} \) of the book. Therefore, the pages left can be expressed as:
\[ \text{Pages left} = x - \frac{7}{9} x \]

### Step 4: Set up the equation
Since we know that the pages left equal 40, we can set up the equation:
\[ x - \frac{7}{9} x = 40 \]

### Step 5: Simplify the equation
To simplify the left side, we can express \( x \) as \( \frac{9}{9} x \):
\[ \frac{9}{9} x - \frac{7}{9} x = 40 \]
This simplifies to:
\[ \frac{2}{9} x = 40 \]

### Step 6: Solve for \( x \)
To find \( x \), multiply both sides by \( \frac{9}{2} \):
\[ x = 40 \times \frac{9}{2} \]
Calculating this gives:
\[ x = 40 \times 4.5 = 180 \]

### Conclusion
Thus, the total number of pages in the book is \( 180 \).

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