To help Joey determine how many weeks he needs to keep his money in the bank until it reaches at least $250, we can set up an inequality based on his starting amount and weekly additions.

Joey has:

• $100 initially
• Adds $25 each week (let $w$ represent the number of weeks)

The condition states he wants his balance to be at least $250. Therefore, we need the inequality:

$100 + 25w \geq 250$

From the choices provided, the correct inequality is: 100 + 25w ≥ 250

This inequality will allow Joey to solve for $w$ to find out how many weeks it will take to reach or exceed $250.

Would you like further details on how to solve this inequality or have any other questions?

Here are some additional questions for exploration:

1. How would you solve the inequality $100 + 25w \geq 250$ for $w$?
2. What would the solution mean in the context of weeks Joey needs?
3. What if Joey wants at least $300? How would the inequality change?
4. How would the inequality change if Joey were adding $30 per week instead?
5. What if Joey starts with $150 instead of $100?

Tip: When solving inequalities, remember that dividing or multiplying by a negative number reverses the inequality sign.