Solve for Equal Files: When File A is 8 Times File B Plus 35 Pages

To solve this problem, we'll perform the following steps:

• Step 1: Define $x$ as the number of pages in file B.
• Step 2: Express the number of pages in file A as $8x$.
• Step 3: Establish the equation based on the problem statement: $8x = x + 35$.
• Step 4: Solve the equation for $x$.
• Step 5: Calculate the number of pages in file A using the relationship $8x$.

Now, let's solve it step by step:
Step 1: Let $x$ represent the number of pages in file B.

Step 2: The number of pages in file A is 8 times that of file B, so it is $8x$.

Step 3: Form the equation based on adding 35 pages to file B: $8x = x + 35$.

Step 4: Solve for $x$:
Subtract $x$ from both sides to consolidate terms:
$8x - x = x + 35 - x$
This simplifies to $7x = 35$.

Step 5: Solve for $x$ by dividing both sides by 7:
$x = \frac{35}{7} = 5$.

Now, substitute back to find the number of pages in file A:
The number of pages in file A is $8x = 8 \times 5 = 40$.

Therefore, the number of pages in file A is $40$.