To determine which ordered pairs represent viable solutions, we need to find pairs [tex]\((x, y)\)[/tex] where:
- [tex]\( x \)[/tex] is the number of days a book is late.
- [tex]\( y \)[/tex] is the total fee calculated by [tex]\( y = x \times 0.30 \)[/tex].
Here are the steps for each pair:
1. Check the pair [tex]\((-3, -0.90)\)[/tex]:
- [tex]\( x = -3 \)[/tex] days
- The fee should be [tex]\( y = -3 \times 0.30 = -0.90 \)[/tex]
- The given [tex]\( y \)[/tex] is [tex]\(-0.90\)[/tex], which matches our calculation.
- Therefore, [tex]\((-3, -0.90)\)[/tex] is a viable solution.
2. Check the pair [tex]\((-2.5, -0.75)\)[/tex]:
- [tex]\( x = -2.5 \)[/tex] days
- The fee should be [tex]\( y = -2.5 \times 0.30 = -0.75 \)[/tex]
- The given [tex]\( y \)[/tex] is [tex]\(-0.75\)[/tex], which matches our calculation.
- Therefore, [tex]\((-2.5, -0.75)\)[/tex] is a viable solution.
3. Check the pair [tex]\((4.5, 1.35)\)[/tex]:
- [tex]\( x = 4.5 \)[/tex] days
- The fee should be [tex]\( y = 4.5 \times 0.30 = 1.35 \)[/tex]
- The given [tex]\( y \)[/tex] is [tex]\(1.35\)[/tex], which matches our calculation.
- Therefore, [tex]\((4.5, 1.35)\)[/tex] is a viable solution.
4. Check the pair [tex]\((8, 2.40)\)[/tex]:
- [tex]\( x = 8 \)[/tex] days
- The fee should be [tex]\( y = 8 \times 0.30 = 2.40 \)[/tex]
- The given [tex]\( y \)[/tex] is [tex]\(2.40\)[/tex], which matches our calculation.
- Therefore, [tex]\((8, 2.40)\)[/tex] is a viable solution.
In summary, all the pairs [tex]\((-3, -0.90)\)[/tex], [tex]\((-2.5, -0.75)\)[/tex], [tex]\((4.5, 1.35)\)[/tex], and [tex]\((8, 2.40)\)[/tex] are viable solutions as the calculated total fee for each pair correctly matches the given value.
