Olivia is organizing a bake sale, and the goal is to raise at least [tex] \$500 [/tex]. So far, [tex] \$210 [/tex] has been raised. If the items are all [tex] \$5 [/tex] each, which inequality represents how many more items need to be sold to meet Olivia's goal?

A. [tex] 5b + 210 \geq 500 [/tex]

B. [tex] b + 500 \geq 210 [/tex]

C. [tex] 5b \geq 500 + 210 [/tex]

D. [tex] 5b + 210 \leq 500 [/tex]

To solve the problem, we need to determine which inequality represents the number of additional items Olivia needs to sell to meet her goal of raising at least [tex]$500.

Here's a step-by-step breakdown:

1. Understand the Current Situation:
- Olivia's goal is to raise at least $[/tex]500.
- So far, she has already raised [tex]$210.

2. Identify What's Needed:
- To achieve the goal of $[/tex]500, Olivia needs to make up the difference between what she has already raised and the goal. This means she needs at least [tex]$500 - $[/tex]210 more to reach the target.

3. Express the Additional Amount Needed:
```
Additional amount needed = [tex]$500 - $[/tex]210 = [tex]$290
```

4. Determine How Many More Items to Sell:
- Each item sold contributes $[/tex]5.
- Let [tex]$ b $[/tex] represent the number of additional items Olivia needs to sell.
- Each item sold brings in [tex]$5, so the total amount from selling $ b $ items is $ 5b $.

5. Set Up the Inequality:
- Since the amount from selling these additional items, $ 5b $, plus the amount already raised, $[/tex]210, needs to be at least $500, the inequality is:
```
5b + 210 \geq 500
```

6. Verify Based on the Options Provided:
The correct inequality from the given options that matches this formulation is:

(A) [tex]$ 5b + 210 \geq 500 $[/tex]

This inequality shows how many additional items Olivia needs to sell to reach her fundraising goal.