Let's analyze and solve the question in the image:

Problem Breakdown:

The mathematical expression describes "The quotient of the sum of 5 and twice a number, and the difference of 10 less than three times the same number."

• Step 1: Translate each part of the description into algebraic expressions.

  • "The sum of 5 and twice a number" → $5 + 2n$
  • "The difference of 10 less than three times the same number" → $3n - 10$

• Step 2: Combine these parts into a quotient.

  • A quotient implies division, so the expression becomes: $\frac{5 + 2n}{3n - 10}$

Correct Answer:

The correct algebraic representation is A. $\frac{5 + 2n}{3n - 10}$.

Would you like a more detailed breakdown or any additional clarifications?

Related Questions:

1. What is the process for identifying parts of a word problem to form algebraic expressions?
2. How do we interpret keywords like "sum," "difference," and "quotient" in math problems?
3. Could the numerator or denominator change if the description was altered slightly?
4. How would this problem differ if the order of terms was reversed?
5. Can you derive a real-world example where a similar quotient might arise?

Tip:

When solving word problems, identify the operation keywords (e.g., "sum," "difference," "quotient") to guide your algebraic translations effectively!