Olivia is organizing a bake sale, and her goal is to raise at least [tex]\$500[/tex]. So far, she has raised [tex]\$210[/tex]. If the items are all [tex]\$5[/tex] each, which inequality represents how many more items she needs to sell to meet her 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]

Let [tex]$ b $[/tex] be the number of additional items Olivia needs to sell. Since each item is sold for \[tex]$5 and Olivia already has \$[/tex]210, the total amount raised after selling [tex]$ b $[/tex] items can be expressed as

[tex]$$5b + 210.$$[/tex]

Olivia's goal is to raise at least \[tex]$500. Therefore, we set up the inequality:

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

To determine the minimum number of items needed, first subtract 210 from both sides:

$[/tex][tex]$5b \geq 500 - 210,$[/tex][tex]$
$[/tex][tex]$5b \geq 290.$[/tex][tex]$

Next, divide both sides by 5 to solve for $ b $:

$[/tex][tex]$b \geq \frac{290}{5},$[/tex][tex]$
$[/tex][tex]$b \geq 58.$[/tex][tex]$

Thus, Olivia needs to sell at least 58 more items to meet the goal.

The inequality that represents this situation is

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