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------------------------------------------------ Olivia is organizing a bake sale, and the goal is to raise at least [tex]\$500[/tex]. So far, they have raised [tex]\$210[/tex]. If the items are all [tex]\$5[/tex] each, which inequality represents how many more items they need to sell 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 determine the inequality that represents how many more items Olivia needs to sell to reach her goal of raising at least [tex]$500, we start by considering the following information:

- Olivia has already raised $[/tex]210.
- Each item they sell raises [tex]$5.
- The goal is to raise at least $[/tex]500.

1. Determine the additional amount needed:
Olivia needs to raise a total of [tex]$500, and since she has already raised $[/tex]210, the additional amount needed is:
[tex]\[
500 - 210 = 290
\][/tex]

2. Set up the inequality for the number of items (b) they need to sell:
Each item sold brings in [tex]$5. If $ b $ is the number of additional items that need to be sold, the total amount raised from selling these additional items is $ 5b $.

We want this amount plus the amount already raised to be at least $[/tex]500. So, the inequality will be:
[tex]\[
5b + 210 \geq 500
\][/tex]

Therefore, the correct inequality is [tex]$ 5b + 210 \geq 500 $[/tex], which matches option (A).

This inequality tells us how many more items Olivia needs to sell to ensure the total amount raised meets or exceeds the $500 goal.