Answer :
To determine the correct algebraic expression for the given phrase "the product of 50 and the number of employees," let's break down the phrase step-by-step:
1. Understanding the Term "Product":
- In mathematics, the term "product" refers to the result of multiplying two numbers together.
2. Identifying the Numbers to be Multiplied:
- The phrase specifies "50" and "the number of employees." Let's denote the number of employees by the variable [tex]\( n \)[/tex].
3. Forming the Multiplication Expression:
- To represent "the product of 50 and [tex]\( n \)[/tex]" algebraically, we multiply 50 by [tex]\( n \)[/tex].
4. Evaluating the Choices:
- Choice A: [tex]\( 50 + n \)[/tex] represents the sum of 50 and [tex]\( n \)[/tex], not the product.
- Choice B: [tex]\( 50 - n \)[/tex] represents the difference between 50 and [tex]\( n \)[/tex], not the product.
- Choice C: [tex]\( 50 \cdot n \)[/tex] correctly represents the product of 50 and [tex]\( n \)[/tex].
- Choice D: [tex]\( \frac{50}{n} \)[/tex] represents the division of 50 by [tex]\( n \)[/tex], not the product.
Based on this reasoning, the correct algebraic expression is [tex]\( 50 \cdot n \)[/tex].
Therefore, the correct choice is:
C. [tex]\( 50 \cdot n \)[/tex]
1. Understanding the Term "Product":
- In mathematics, the term "product" refers to the result of multiplying two numbers together.
2. Identifying the Numbers to be Multiplied:
- The phrase specifies "50" and "the number of employees." Let's denote the number of employees by the variable [tex]\( n \)[/tex].
3. Forming the Multiplication Expression:
- To represent "the product of 50 and [tex]\( n \)[/tex]" algebraically, we multiply 50 by [tex]\( n \)[/tex].
4. Evaluating the Choices:
- Choice A: [tex]\( 50 + n \)[/tex] represents the sum of 50 and [tex]\( n \)[/tex], not the product.
- Choice B: [tex]\( 50 - n \)[/tex] represents the difference between 50 and [tex]\( n \)[/tex], not the product.
- Choice C: [tex]\( 50 \cdot n \)[/tex] correctly represents the product of 50 and [tex]\( n \)[/tex].
- Choice D: [tex]\( \frac{50}{n} \)[/tex] represents the division of 50 by [tex]\( n \)[/tex], not the product.
Based on this reasoning, the correct algebraic expression is [tex]\( 50 \cdot n \)[/tex].
Therefore, the correct choice is:
C. [tex]\( 50 \cdot n \)[/tex]
