Question

linda wants to save $900 to buy a tv. she saves $17 each week. the amount, a (in dollars), that she still needs after w weeks is given by the following function.
a(w) = 900 - 17w
answer the following questions.
(a) if linda still needs $611, how many weeks has she been saving?
weeks
(b) how much money does linda still need after 7 weeks?
$

Explanation:

Part (a)

Step 1: Set up the equation

We know the function \( A(w) = 900 - 17w \), and we are given that \( A(w)=611 \). So we set up the equation:
\( 611 = 900 - 17w \)

Step 2: Solve for \( w \)

First, subtract 900 from both sides:
\( 611 - 900 = -17w \)
\( -289 = -17w \)

Then, divide both sides by -17:
\( w=\frac{-289}{-17} = 17 \)

Part (b)

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

We use the function \( A(w)=900 - 17w \) and substitute \( w = 7 \):
\( A(7)=900 - 17\times7 \)

Step 2: Calculate the value

First, calculate \( 17\times7 = 119 \)
Then, subtract from 900:
\( A(7)=900 - 119 = 781 \)

Answer:

(a) \(\boldsymbol{17}\) weeks
(b) \(\boldsymbol{781}\) dollars