Question

suppose your club is selling candles to raise money. it cost $100 to rent a booth from which to sell the candles. if the candles cost your club $1 each and are sold for $5, how many candles must be sold to equal your expenses?

Explanation:

Step1: Set up cost - revenue equation

Let $x$ be the number of candles sold. The total cost $C$ is the sum of the booth - rent cost and the cost of the candles. So $C = 100+1x$. The total revenue $R$ from selling $x$ candles at $5$ dollars each is $R = 5x$. We want to find $x$ when $R = C$, so the equation is $5x=100 + x$.

Step2: Solve the equation for $x$

Subtract $x$ from both sides of the equation $5x=100 + x$. We get $5x−x=100$, which simplifies to $4x = 100$.

Step3: Isolate $x$

Divide both sides of the equation $4x = 100$ by $4$. So $x=\frac{100}{4}=25$.

Answer:

25