To determine which ordered pair is a viable solution, we need to check if the fee calculation holds true based on the given rule: a $0.30 fee is charged each day a book is late.
The relationship between the number of days late, \( x \), and the total fee, \( y \), can be expressed with the equation:
\[ y = 0.30x \]
We'll check each ordered pair \((x, y)\) to see if it satisfies this equation:
1. \((-3, -0.90)\)
\[ y = 0.30(-3) = -0.90 \]
This ordered pair satisfies the equation.
2. \((-2.5, -0.75)\)
\[ y = 0.30(-2.5) = -0.75 \]
This ordered pair satisfies the equation.
3. \((4.5, 1.35)\)
\[ y = 0.30(4.5) = 1.35 \]
This ordered pair satisfies the equation.
4. \((8, 2.40)\)
\[ y = 0.30(8) = 2.40 \]
This ordered pair satisfies the equation.
Now, considering the context (fees for overdue books), values of \( x \) and \( y \) must be non-negative since you cannot have negative or fractional days for the books to be overdue, nor negative or fractional fees in such a context.
- \((-3, -0.90)\): Not valid, as \( x \) cannot be negative.
- \((-2.5, -0.75)\): Not valid, as \( x \) cannot be negative or fractional.
- \((4.5, 1.35)\): Not valid, as \( x \) cannot be fractional.
- \((8, 2.40)\): Valid, as both \( x \) and \( y \) are non-negative and integers.
Therefore, the only viable solution in this context is \((8, 2.40)\).
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?
(–3, –0.90)
(–2.5, –0.75)
(4.5, 1.35)
(8, 2.40)
1 answer
5 answers