To determine how many candles the drama club must sell to make more than [tex]$125 in profit, we start by defining the profit.
1. Cost of Candles: They spend $[/tex]100 upfront on the candles.
2. Selling Price: They sell each candle for [tex]$4.50.
3. Profit Calculation: Profit is calculated as the total revenue minus the total cost.
Given:
- Total revenue from selling \( x \) candles is \( 4.5x \) dollars.
- Total cost is \( 100 \) dollars.
- We want the profit to be more than \( 125 \) dollars.
The inequality representing the profit being more than $[/tex]125 can be expressed as:
[tex]\[
4.5x - 100 > 125
\][/tex]
This inequality states that the revenue minus the initial cost should be greater than the desired profit of $125.
We can solve this inequality step-by-step:
1. Start with the inequality:
[tex]\[
4.5x - 100 > 125
\][/tex]
2. Add [tex]\( 100 \)[/tex] to both sides of the inequality to get rid of the constant term on the left side:
[tex]\[
4.5x - 100 + 100 > 125 + 100
\][/tex]
Simplifying, we get:
[tex]\[
4.5x > 225
\][/tex]
3. Finally, divide both sides by [tex]\( 4.5 \)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[
x > \frac{225}{4.5}
\][/tex]
Simplifying the division:
[tex]\[
x > 50
\][/tex]
Therefore, the drama club must sell more than [tex]\( 50 \)[/tex] candles to make more than [tex]\( 125 \)[/tex] dollars in profit. The correct inequality to use is:
[tex]\[
4.5x - 100 > 125
\][/tex]
So, the first option [tex]\( 4.5x - 100 > 125 \)[/tex] is the correct inequality to find [tex]\( x \)[/tex].
