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

1 answer

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 \( c = 18 + 4x \).