Question
Parts of algebraic expressions practice using the equation c = 18 + 4x which of the following statements could be correct interpretation of the coefficient of a term statement 1 can you spent $4 per paper back at the public library statement too 10 minutes per book at the public library
Answers
GPT-4o mini
In the equation \( c = 18 + 4x \), the term \( 4x \) represents a linear relationship between two variables. Here, \( c \) denotes a total cost, and \( x \) denotes the number of items (for example, books or paperbacks).
In this context:
- The **constant term** \( 18 \) represents a fixed cost, which could be interpreted as an initial fee or base cost associated with purchasing or borrowing the books.
- The **coefficient** \( 4 \) indicates a variable cost that is dependent on how many items (books) are involved.
### Interpretation of Coefficient:
- **Statement 1:** "You can spend $4 per paperback at the public library."
- **Correct Interpretation:** This statement correctly interprets the coefficient \( 4 \) as the cost associated with each paperback (hence it's the variable cost incurred for each additional book).
- **Statement 2:** "10 minutes per book at the public library."
- **Incorrect Interpretation:** This statement does not correspond with the meaning of the coefficient \( 4 \) in the context of the equation, as it relates to a time duration rather than a monetary cost.
### Conclusion:
Only **Statement 1** could be a correct interpretation of the coefficient \( 4 \) in the equation \( c = 18 + 4x \).
In this context:
- The **constant term** \( 18 \) represents a fixed cost, which could be interpreted as an initial fee or base cost associated with purchasing or borrowing the books.
- The **coefficient** \( 4 \) indicates a variable cost that is dependent on how many items (books) are involved.
### Interpretation of Coefficient:
- **Statement 1:** "You can spend $4 per paperback at the public library."
- **Correct Interpretation:** This statement correctly interprets the coefficient \( 4 \) as the cost associated with each paperback (hence it's the variable cost incurred for each additional book).
- **Statement 2:** "10 minutes per book at the public library."
- **Incorrect Interpretation:** This statement does not correspond with the meaning of the coefficient \( 4 \) in the context of the equation, as it relates to a time duration rather than a monetary cost.
### Conclusion:
Only **Statement 1** could be a correct interpretation of the coefficient \( 4 \) in the equation \( c = 18 + 4x \).