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

Q: What's the difference between '8 times greater' and '8 times as much'?

They mean the same thing in math problems! Both phrases translate to $ A = 8B $. Don't overthink the wording - focus on the mathematical relationship.

Q: Why do we set up the equation as 8x = x + 35?

Because when File B gets 35 more pages, it will have $ x + 35 $ pages. Since both files will then be equal, we set File A's pages $ (8x) $ equal to File B's new total.

Q: How do I know which file to call 'x'?

Always let x represent the smaller quantity! Since File B has fewer pages than File A, let $ x $ be File B's pages. This makes the math simpler.

Q: Can I solve this problem differently?

Yes! You could let $ y $ represent File A's pages, then File B has $ \frac{y}{8} $ pages. But using the smaller quantity as your variable typically makes calculations easier.

Linear Equations with Word Problem Context

The number of pages in file A is 8 times greater than the number of pages in file B.

If we add 35 pages to file B, both files will have the same number of pages.

Calculate the number of pages in file A.

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Step-by-step solution

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 $40$ .

Final Answer

$40$

Key Points to Remember

Essential concepts to master this topic

Variable Definition: Let x represent the smaller unknown quantity first
Translation: '8 times greater' means 8x, 'same pages' means 8x = x + 35
Verification: File A has 40 pages, File B + 35 = 5 + 35 = 40 ✓

Common Mistakes

Avoid these frequent errors

Confusing '8 times greater' with '8 times as much as'
Don't write A = 8B + something when it says 'A is 8 times greater than B' = wrong setup! This misinterprets the relationship and leads to incorrect equations. Always read 'X times greater than Y' as simply X times Y, so A = 8B.

Practice Quiz

Test your knowledge with interactive questions

$$ 11=a-16 $$

$a=\text{?}$

FAQ

Everything you need to know about this question

What's the difference between '8 times greater' and '8 times as much'?

They mean the same thing in math problems! Both phrases translate to $A = 8B$ . Don't overthink the wording - focus on the mathematical relationship.

Why do we set up the equation as 8x = x + 35?

Because when File B gets 35 more pages, it will have $x + 35$ pages. Since both files will then be equal, we set File A's pages $(8x)$ equal to File B's new total.

How do I know which file to call 'x'?

Always let x represent the smaller quantity! Since File B has fewer pages than File A, let $x$ be File B's pages. This makes the math simpler.

What if I get a negative answer?

Check your equation setup! In real-world problems like file pages, negative answers usually mean you made an error in translating the word problem into math.

Can I solve this problem differently?

Yes! You could let $y$ represent File A's pages, then File B has $\frac{y}{8}$ pages. But using the smaller quantity as your variable typically makes calculations easier.

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