To determine which ordered pair [tex]\((x, y)\)[/tex] is a viable solution to the problem where [tex]\(x\)[/tex] represents the number of days a library book is late and [tex]\(y\)[/tex] represents the total fee, we need to evaluate whether [tex]\(y = 0.30 \cdot x\)[/tex] holds true for each pair.
Let's examine each ordered pair:
1. For [tex]\((-3, -0.90)\)[/tex]:
- Calculate the expected fee: [tex]\(0.30 \times -3 = -0.90\)[/tex]
- Compare with the given [tex]\(y\)[/tex]: [tex]\(-0.90 = -0.90\)[/tex]
- This pair is viable.
2. For [tex]\((-2.5, -0.75)\)[/tex]:
- Calculate the expected fee: [tex]\(0.30 \times -2.5 = -0.75\)[/tex]
- Compare with the given [tex]\(y\)[/tex]: [tex]\(-0.75 = -0.75\)[/tex]
- This pair is viable.
3. For [tex]\((4.5, 1.35)\)[/tex]:
- Calculate the expected fee: [tex]\(0.30 \times 4.5 = 1.35\)[/tex]
- Compare with the given [tex]\(y\)[/tex]: [tex]\(1.35 = 1.35\)[/tex]
- This pair is viable.
4. For [tex]\((8, 2.40)\)[/tex]:
- Calculate the expected fee: [tex]\(0.30 \times 8 = 2.40\)[/tex]
- Compare with the given [tex]\(y\)[/tex]: [tex]\(2.40 = 2.40\)[/tex]
- This pair is viable.
Therefore, analyzing these pairs:
- Negative days and negative fees make physical sense in real-world conditions where a library fee system considers only non-negative days.
- Hence, focusing on non-negative days, we can conclude that [tex]\((8, 2.40)\)[/tex] is the most appropriate viable solution.
The viable solution from the given pairs is:
[tex]\[
(8, 2.40)
\][/tex]
