To determine which algebraic expression represents the phrase "the product of 34 and the number of pounds," let's break down the phrase step by step.
1. Understand the key terms in the phrase:
- Product: This indicates a multiplication operation.
- 34: This is one of the factors in the multiplication.
- Number of pounds: Let’s denote the number of pounds by the variable \( p \).
2. Construct the expression:
- The product of 34 and the number of pounds means we need to multiply 34 by the variable \( p \).
3. Look at the given choices:
- A. \( 34 - p \): This represents the difference (subtraction) between 34 and \( p \), not a product.
- B. \( \frac{34}{p} \): This represents the division of 34 by \( p \), not a product.
- C. \( 34 \cdot p \): This correctly represents the multiplication (product) of 34 and \( p \).
- D. \( 34 + p \): This represents the sum (addition) of 34 and \( p \), not a product.
4. Identify the correct expression:
- The correct expression that represents "the product of 34 and the number of pounds" is \( 34 \cdot p \).
Therefore, the correct answer is:
C. [tex]\( 34 \cdot p \)[/tex]
