To determine which ordered pair [tex]\((x, y)\)[/tex] is a viable solution, we need to check if the given fee per day and the total fee match. Here, [tex]\(x\)[/tex] represents the number of days a book is late and [tex]\(y\)[/tex] represents the total fee. The daily fee is \$0.30.
Let's evaluate each ordered pair:
1. For [tex]\((-3, -0.90)\)[/tex]:
[tex]\[
\text{Total fee} = 0.30 \times (-3) = -0.90
\][/tex]
The calculated total fee is [tex]\(-0.90\)[/tex], which matches the given [tex]\(y\)[/tex] value in the ordered pair. Therefore, [tex]\((-3, -0.90)\)[/tex] is a viable solution.
2. For [tex]\((-2.5, -0.75)\)[/tex]:
[tex]\[
\text{Total fee} = 0.30 \times (-2.5) = -0.75
\][/tex]
The calculated total fee is [tex]\(-0.75\)[/tex], which matches the given [tex]\(y\)[/tex] value in the ordered pair. Therefore, [tex]\((-2.5, -0.75)\)[/tex] is a viable solution.
3. For [tex]\((4.5, 1.35)\)[/tex]:
[tex]\[
\text{Total fee} = 0.30 \times 4.5 = 1.35
\][/tex]
The calculated total fee is [tex]\(1.35\)[/tex], which matches the given [tex]\(y\)[/tex] value in the ordered pair. Therefore, [tex]\((4.5, 1.35)\)[/tex] is a viable solution.
4. For [tex]\((8, 2.40)\)[/tex]:
[tex]\[
\text{Total fee} = 0.30 \times 8 = 2.40
\][/tex]
The calculated total fee is [tex]\(2.40\)[/tex], which matches the given [tex]\(y\)[/tex] value in the ordered pair. Therefore, [tex]\((8, 2.40)\)[/tex] is a viable solution.
Based on the calculations, the viable solutions are:
- [tex]\((-2.5, -0.75)\)[/tex]
- [tex]\((8, 2.40)\)[/tex]
