Let's analyze Aaliyah's savings plan and identify the error in the table provided.
First, we start with the equation given:
[tex]\[ t = 25 + 8.25w \][/tex]
Where:
- [tex]\( w \)[/tex] represents the number of weeks.
- [tex]\( t \)[/tex] represents the total amount Aaliyah has saved.
Let's examine each entry in the table to ensure they are correct.
1. For [tex]\( w = 12 \)[/tex]:
[tex]\[ t = 25 + 8.25 \times 12 \][/tex]
[tex]\[ t = 25 + 99 = 124 \][/tex]
The pair is [tex]\((12, 124)\)[/tex], which matches the table.
2. For [tex]\( w = 13 \)[/tex]:
[tex]\[ t = 25 + 8.25 \times 13 \][/tex]
[tex]\[ t = 25 + 107.25 = 132.25 \][/tex]
The correct ordered pair should be [tex]\((13, 132.25)\)[/tex].
3. For [tex]\( w = 14 \)[/tex]:
[tex]\[ t = 25 + 8.25 \times 14 \][/tex]
[tex]\[ t = 25 + 115.5 = 140.5 \][/tex]
The pair is [tex]\((14, 140.5)\)[/tex], which matches the table.
4. For [tex]\( w = 15 \)[/tex]:
[tex]\[ t = 25 + 8.25 \times 15 \][/tex]
[tex]\[ t = 25 + 123.75 = 148.75 \][/tex]
The pair is [tex]\((15, 148.75)\)[/tex], which matches the table.
By comparing the calculated values with the provided table, we can identify that the error is in the ordered pair for [tex]\( w = 13 \)[/tex]. The table entry shows [tex]\((132.25, 13)\)[/tex], while it should be [tex]\((13, 132.25)\)[/tex].
Therefore, the correct error is:
The ordered pair [tex]\((132.25, 13)\)[/tex] should be [tex]\((13, 132.25)\)[/tex].
