Question
Jamal bakes cookies and sells them at a local market. He uses the equation P = 3n − (1.2n + 20) to determine his total profit, in dollars, when he sells n batches of cookies. Based on this equation, how much does he charge for each batch of cookies?
Answers
GPT-4o mini
The given equation for Jamal's total profit is:
\[ P = 3n - (1.2n + 20) \]
To find out how much Jamal charges for each batch of cookies, we need to analyze the equation. The equation can be simplified as follows:
1. Distribute the negative sign:
\[ P = 3n - 1.2n - 20 \]
2. Combine like terms:
\[ P = (3n - 1.2n) - 20 \]
\[ P = 1.8n - 20 \]
In this context:
- \( 1.8n \) represents the total revenue from selling \( n \) batches of cookies, assuming he charges \( 3 \) dollars per batch.
- \( 20 \) could represent fixed costs or initial expenses that must be paid regardless of the number of batches sold.
From the equation, the profit \( P \) after accounting for costs is influenced by both the revenue from the sales and the fixed costs. When \( n = 1 \), the profit can help infer how much he charges per batch.
Since Jamal charges $3 for each batch, that value is consistent with the total revenue from selling \( n \) batches being \( 3n \).
Thus, Jamal charges **$3 for each batch of cookies**.
\[ P = 3n - (1.2n + 20) \]
To find out how much Jamal charges for each batch of cookies, we need to analyze the equation. The equation can be simplified as follows:
1. Distribute the negative sign:
\[ P = 3n - 1.2n - 20 \]
2. Combine like terms:
\[ P = (3n - 1.2n) - 20 \]
\[ P = 1.8n - 20 \]
In this context:
- \( 1.8n \) represents the total revenue from selling \( n \) batches of cookies, assuming he charges \( 3 \) dollars per batch.
- \( 20 \) could represent fixed costs or initial expenses that must be paid regardless of the number of batches sold.
From the equation, the profit \( P \) after accounting for costs is influenced by both the revenue from the sales and the fixed costs. When \( n = 1 \), the profit can help infer how much he charges per batch.
Since Jamal charges $3 for each batch, that value is consistent with the total revenue from selling \( n \) batches being \( 3n \).
Thus, Jamal charges **$3 for each batch of cookies**.