Answer :
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]$
[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]$