To find the correct algebraic expression, let's break down the phrase step-by-step:
1. Identify the operation needed:
- The phrase "the product of" implies multiplication.
2. Identify the variables involved:
- We have the number "67."
- We have "the number of weeks," which we can denote by the variable [tex]\( w \)[/tex].
3. Combine the elements:
- To represent "the product of 67 and the number of weeks," we multiply 67 by [tex]\( w \)[/tex].
By following these steps, we see that the phrase translates to the algebraic expression [tex]\( 67 \cdot w \)[/tex].
Now, let's match this with the given options:
- A. [tex]\( 67 + w \)[/tex]: This represents the sum, not the product.
- B. [tex]\( 67 \cdot w \)[/tex]: This correctly represents the product of 67 and [tex]\( w \)[/tex].
- C. [tex]\( \frac{67}{w} \)[/tex]: This represents the quotient, not the product.
- D. [tex]\( 67 - w \)[/tex]: This represents the difference, not the product.
Therefore, the correct answer is:
B. [tex]\( 67 \cdot w \)[/tex]
