To determine how many weeks it will take Aaliyah to save enough money to buy a television that costs $135.75, we start with the given equation for her savings plan:
[tex]\[ t = 25 + 8.25w \][/tex]
where [tex]\( t \)[/tex] is the total amount of money saved and [tex]\( w \)[/tex] is the number of weeks she saves.
We need to find [tex]\( w \)[/tex] when [tex]\( t = 135.75 \)[/tex]. So, we set up the equation:
[tex]\[ 135.75 = 25 + 8.25w \][/tex]
To solve for [tex]\( w \)[/tex], follow these steps:
1. Subtract 25 from both sides of the equation to isolate the term involving [tex]\( w \)[/tex]:
[tex]\[ 135.75 - 25 = 8.25w \][/tex]
[tex]\[ 110.75 = 8.25w \][/tex]
2. Next, divide both sides by 8.25 to solve for [tex]\( w \)[/tex]:
[tex]\[ \frac{110.75}{8.25} = w \][/tex]
This gives us:
[tex]\[ w \approx 13.424242424242424 \][/tex]
Rounding to two decimal places, [tex]\( w \approx 13.42 \)[/tex].
Thus, it will take Aaliyah approximately 13.42 weeks to save enough money to buy the television.
