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Answer :
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.
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.
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