Question

jenny wants to save $600 to buy a tv. she saves $19 each week. the amount, a (in dollars), that she still needs after w weeks is given by the following function.
\\( a(w) = 600 - 19w \\)
answer the following questions.
(a) if jenny still needs $258, how many weeks has she been saving?
\\( \square \\) weeks
(b) how much money does jenny still need after 7 weeks?
$\square

Explanation:

Part (a)

Step 1: Set up the equation

We know that \( A(w) = 600 - 19w \), and we are given that \( A(w)=258 \). So we set up the equation \( 258=600 - 19w \).

Step 2: Solve for \( w \)

First, we subtract 600 from both sides: \( 258-600=- 19w \), which simplifies to \( - 342=-19w \). Then we divide both sides by - 19: \( w=\frac{-342}{-19} = 18 \).

Part (b)

Step 1: Substitute \( w = 7 \) into the function

We have the function \( A(w)=600 - 19w \). Substitute \( w = 7 \) into it: \( A(7)=600-19\times7 \).

Step 2: Calculate the value

First, calculate \( 19\times7 = 133 \). Then, \( A(7)=600 - 133=467 \).

Answer:

(a) \(\boldsymbol{18}\) weeks
(b) \(\boldsymbol{467}\) dollars