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Answer :
Certainly! Let's solve the problem step-by-step to determine which inequality represents how many more items Olivia needs to sell to meet her goal.
1. Identify the Goal and Current Achievement:
- Olivia wants to raise at least [tex]$500.
- So far, she has raised $[/tex]210.
2. Determine the Additional Amount Needed:
- To find out how much more money Olivia needs, subtract the amount she has already raised from her goal:
[tex]\[
\text{Additional amount needed} = 500 - 210 = 290
\][/tex]
3. Determine the Cost of Each Item:
- Each item is sold for [tex]$5.
4. Set Up the Inequality:
- We need to find the minimum number of items, \( b \), that Olivia needs to sell to raise at least an additional $[/tex]290.
- The total money raised from selling [tex]\( b \)[/tex] more items at [tex]$5 each should be at least $[/tex]290:
[tex]\[
5b \geq 290
\][/tex]
5. Identify the Correct Inequality:
- The inequality in the options that represents this is:
[tex]\[
5b + 210 \geq 500
\][/tex]
- This is essentially combining the total raised so far ($210) with the additional amount raised from selling [tex]\( b \)[/tex] items, which matches Option (A).
Therefore, the correct inequality is (A) [tex]\( 5b + 210 \geq 500 \)[/tex].
1. Identify the Goal and Current Achievement:
- Olivia wants to raise at least [tex]$500.
- So far, she has raised $[/tex]210.
2. Determine the Additional Amount Needed:
- To find out how much more money Olivia needs, subtract the amount she has already raised from her goal:
[tex]\[
\text{Additional amount needed} = 500 - 210 = 290
\][/tex]
3. Determine the Cost of Each Item:
- Each item is sold for [tex]$5.
4. Set Up the Inequality:
- We need to find the minimum number of items, \( b \), that Olivia needs to sell to raise at least an additional $[/tex]290.
- The total money raised from selling [tex]\( b \)[/tex] more items at [tex]$5 each should be at least $[/tex]290:
[tex]\[
5b \geq 290
\][/tex]
5. Identify the Correct Inequality:
- The inequality in the options that represents this is:
[tex]\[
5b + 210 \geq 500
\][/tex]
- This is essentially combining the total raised so far ($210) with the additional amount raised from selling [tex]\( b \)[/tex] items, which matches Option (A).
Therefore, the correct inequality is (A) [tex]\( 5b + 210 \geq 500 \)[/tex].
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