Writer A vs Writer B: Fractional Page Output Analysis

Fractional Inequalities with Combined Variables

Writer A writes 35 \frac{3}{5} of the number of pages writer B writes per day. Both of them together write more than 200 pages per day.

What can be said about the number of pages that writer A writes per day?

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1

Understand the problem

Writer A writes 35 \frac{3}{5} of the number of pages writer B writes per day. Both of them together write more than 200 pages per day.

What can be said about the number of pages that writer A writes per day?

2

Step-by-step solution

To solve the problem, we need to analyze the inequality involving the pages written by Writers A and B:

First, let xx represent the number of pages Writer B writes per day. Then, the number of pages Writer A writes is given by the expression 35x\frac{3}{5}x.

The problem states that together they write more than 200 pages per day. Therefore, we can set up the inequality:

35x+x>200. \frac{3}{5}x + x > 200.

We need to simplify and solve this inequality:

  • Combine the terms on the left-hand side:
35x+55x=85x. \frac{3}{5}x + \frac{5}{5}x = \frac{8}{5}x.

Substituting this back into the inequality:

85x>200. \frac{8}{5}x > 200.

To solve for xx, multiply both sides of the inequality by 58\frac{5}{8} to isolate xx:

x>200×58. x > \frac{200 \times 5}{8}.

Perform the multiplication:

x>10008=125. x > \frac{1000}{8} = 125.

This implies that the number of pages xx written by Writer B should be greater than 125.

Substitute x>125x > 125 back to find the pages written by Writer A:

Pages by A=35xPages by A>35125=75. \text{Pages by A} = \frac{3}{5}x \quad \Rightarrow \quad \text{Pages by A} > \frac{3}{5} \cdot 125 = 75.

Therefore, Writer A writes more than 75 pages per day.

The correct answer is:

More than -75

3

Final Answer

More than 75

Key Points to Remember

Essential concepts to master this topic
  • Setup: Define variables for both writers using given fractional relationship
  • Technique: Combine like terms: 35x+x=85x \frac{3}{5}x + x = \frac{8}{5}x
  • Check: Verify 35×125=75 \frac{3}{5} \times 125 = 75 and 75 + 125 > 200 ✓

Common Mistakes

Avoid these frequent errors
  • Adding fractions incorrectly when combining terms
    Don't add 35x+x \frac{3}{5}x + x as 45x \frac{4}{5}x = wrong total! This ignores that x equals 55x \frac{5}{5}x . Always convert whole numbers to fractions with common denominators before adding.

Practice Quiz

Test your knowledge with interactive questions

Solve the following inequality:

\( 3x+4 \leq 10 \)

FAQ

Everything you need to know about this question

Why do I need to write x as a fraction when adding to 3/5x?

+

Because you can't add fractions with different denominators! Think of x as 55x \frac{5}{5}x , so 35x+55x=85x \frac{3}{5}x + \frac{5}{5}x = \frac{8}{5}x .

How do I solve inequalities with fractions?

+

Treat them like equations, but keep the inequality sign! Multiply both sides by the reciprocal: 85x>200 \frac{8}{5}x > 200 becomes x>200×58 x > 200 \times \frac{5}{8} .

Why is the answer 'more than 75' instead of exactly 75?

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Because we have an inequality (>) not an equation (=)! Since Writer B writes more than 125 pages, Writer A writes more than 75 pages.

What if Writer A wrote more pages than Writer B?

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The problem states Writer A writes 35 \frac{3}{5} of Writer B's pages. Since 35<1 \frac{3}{5} < 1 , Writer A always writes fewer pages than Writer B.

Can I check my answer by trying specific numbers?

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Yes! Try Writer B = 130 pages. Then Writer A = 35×130=78 \frac{3}{5} \times 130 = 78 pages. Total: 130 + 78 = 208 > 200 ✓

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