Question
Ethan makes candles and sells them at a holiday market. He uses the equation
P = 10.5n − (4n + 25)
to determine his total profit, in dollars, when he sells n candles.
Based on this equation, how much does he charge for each candle?
P = 10.5n − (4n + 25)
to determine his total profit, in dollars, when he sells n candles.
Based on this equation, how much does he charge for each candle?
Answers
GPT-4o mini
To determine how much Ethan charges for each candle, we first need to simplify the given profit equation:
\[
P = 10.5n - (4n + 25)
\]
Distributing the negative sign:
\[
P = 10.5n - 4n - 25
\]
Now combine like terms:
\[
P = (10.5n - 4n) - 25
\]
\[
P = 6.5n - 25
\]
In this equation, \(P\) represents the total profit, and \(n\) is the number of candles sold. The term \(6.5n\) represents the revenue from selling \(n\) candles, where \(6.5\) is the price per candle.
Therefore, Ethan charges **$6.50 per candle**.
\[
P = 10.5n - (4n + 25)
\]
Distributing the negative sign:
\[
P = 10.5n - 4n - 25
\]
Now combine like terms:
\[
P = (10.5n - 4n) - 25
\]
\[
P = 6.5n - 25
\]
In this equation, \(P\) represents the total profit, and \(n\) is the number of candles sold. The term \(6.5n\) represents the revenue from selling \(n\) candles, where \(6.5\) is the price per candle.
Therefore, Ethan charges **$6.50 per candle**.