Let's break down the problem from the image step by step:

Problem Description:

• Initial deposit: Priya starts with $50 in her bank account.
• Weekly deposit: She deposits $20 each week for 12 weeks.

Part (a): Write an equation for the relationship.

Let:

• $y$ = amount of money in the bank account after $x$ weeks.

At week 0, Priya has $50, and she adds $20 every week. So, the equation would be:

$y = 20x + 50$

where:

• $y$ is the total amount of money in the bank,
• $x$ is the number of weeks,
• $50 is the initial amount,
• $20 is the weekly deposit.

Part (b): Graphing and the amount after 3 weeks.

To graph this equation, the line starts at $y = 50$ (the initial amount) and has a slope of 20, meaning the amount increases by $20 each week.

For 3 weeks, substitute $x = 3$ into the equation:

$y = 20(3) + 50 = 60 + 50 = 110$

Thus, after 3 weeks, Priya has $110 in her account. On the graph, this would be the point $(3, 110)$.

Part (c): How many weeks to reach $250.

Set $y = 250$ in the equation and solve for $x$:

$250 = 20x + 50$ $250 - 50 = 20x$ $200 = 20x$ $x = \frac{200}{20} = 10$

It will take Priya 10 weeks to have $250 in her account.

Would you like any more details on this solution?

Here are some related questions:

1. What would the equation look like if Priya increased her weekly deposit to $25?
2. How much would Priya have after 8 weeks of saving?
3. What is the slope of the equation and what does it represent in this context?
4. How long will it take Priya to save $500?
5. If Priya withdraws $30 after 6 weeks, how does that change her equation?

Tip:

When working with linear equations, always check the slope to understand how fast the quantity changes over time.