Get expert advice and community support for your questions on IDNLearn.com. Our Q&A platform is designed to provide quick and accurate answers to any questions you may have.

The drama club is selling candles for a fundraiser. They spend [tex]$\$100$[/tex] on the candles and sell them for [tex]$\[tex]$4.50$[/tex][/tex] each. How many candles must they sell to make more than [tex]$\$125$[/tex] profit?

Let [tex]$x$[/tex] represent the number of candles sold. Which inequality can you use to find [tex]$x$[/tex]?

A. [tex]4.5x - 100 \ \textgreater \ 125[/tex]
B. [tex]4.5x + 125 \ \textgreater \ 100[/tex]
C. [tex]100 - 4.5x \ \textgreater \ 125[/tex]
D. [tex]100 + 4.5x \ \textgreater \ 125[/tex]


Sagot :

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].
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.