each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. which ordered…

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)

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)

Answer

Explanation:

Step1: Analyze the nature of variables

The number of days $x$ a book is late cannot be negative or a non - whole number in this context (you can't have negative days late or half - days in terms of late fees being charged incrementally per day). The relationship between the number of days late $x$ and the total fee $y$ is $y = 0.3x$.

Step2: Check each option

  • Option 1: $x=-3,y = - 0.90$. Since $x$ (number of days late) is negative, it's not viable.
  • Option 2: $x=-2.5,y=-0.75$. $x$ is negative and non - whole, not viable.
  • Option 3: $x = 4.5,y=1.35$. $x$ is non - whole, not viable as the fee is charged per full day.
  • Option 4: For $x = 8$, using the formula $y=0.3x$, we have $y=0.3\times8=2.40$. This is a viable pair as $x$ is a non - negative whole number and $y$ is calculated correctly using the relationship $y = 0.3x$.

Answer:

D. (8, 2.40)