Assume that the number of overdue days for the library book is X, and the total fine is Y.
Liability charges a fee of $0.30 per day for lateness,
Thus, for one day late, the fee equals: 1 * $0.30
For X days late, the fee becomes: X * $0.30.
The total fee Y corresponds to being X days late, so: Y = 0.30 * X.
Next, we'll verify which possible answers satisfy the equation Y = 0.30 * X.
Options one (-3, -0.9) and two (-2.5, -0.75) are invalid since the number of late days cannot be negative, and these give negative values for X.
Option three (4.5, 1.35) is also incorrect because the library charges per whole day; 4.5 days is not an integer, so they would charge 4 or 5 days, not 4.5.
Option four (8, 2.40) matches the equation perfectly:
Y = 0.30 * X
2.40 = 0.30 * 8
2.40 = 2.40.
Therefore, the only correct answer is option four (8, 2.40).
