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Answer :
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.
- 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.
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