Question

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, 1.20)
○ (8, 2.40)

Explanation:

Step1: Analyze the domain of x

The number of days late \( x \) cannot be negative or a non - integer in the context of library late fees (you can't be late a negative number of days, and the fee is charged per day at midnight, so partial days don't make sense for the number of days late in terms of the fee structure). So \( x\geq0 \) and \( x \) should be a non - negative integer.

Step2: Check each ordered pair

• For \((- 3,-0.90)\): \( x=-3\) is negative, so this is not a viable solution.
• For \((-2.5,-0.75)\): \( x = - 2.5\) is negative, so this is not a viable solution.
• For \((4.5,1.20)\): \( x = 4.5\) is not an integer. Since the fee is charged per day at midnight, the number of days late should be a whole number (you can't have half a day of being late in the sense of the daily fee charge at midnight).
• For \((8,2.40)\): First, check the value of \( x = 8\) (which is a non - negative integer). Then, the total fee \( y\) should be \( y=0.30x\). Substitute \( x = 8\) into the formula: \( y=0.30\times8 = 2.40\), which matches the ordered pair.

Answer:

D. \((8, 2.40)\)