Let’s solve the questions in the uploaded image:

Problem Breakdown:

The equation provided is:

$A(w) = 700 - 18w$

where:

• $A(w)$ is the amount (in dollars) that Bill still needs to save.
• $w$ is the number of weeks Bill has been saving.

Part (a):

If Bill still needs $358, how many weeks has he been saving?

Set $A(w) = 358$ and solve for $w$: $358 = 700 - 18w$ Rearrange: $18w = 700 - 358$ $18w = 342$ $w = \frac{342}{18} = 19$

So, Bill has been saving for 19 weeks.

Part (b):

How much money does Bill still need after 7 weeks?

Substitute $w = 7$ into the equation: $A(7) = 700 - 18(7)$ $A(7) = 700 - 126$ $A(7) = 574$

So, Bill still needs $574 after 7 weeks.

Would you like additional explanation or further clarification? Here are some related questions to consider:

1. How does the rate of savings ($18 per week) impact the time needed to reach $700?
2. What would the equation look like if Bill increased his savings rate to $25 per week?
3. How many total weeks would it take Bill to save exactly $700?
4. If Bill started with $100 already saved, how would this change the equation?
5. What is the maximum number of weeks Bill could save while still needing more than $0?

Tip: When working with linear equations in real-life problems, identify the rate (slope) and starting point (intercept) to simplify your calculations.