Samantha makes unique bracelets. For a pack of materials she spends 300 dollars and hopes to make 900 dollars in profit. She writes the inequality Pn-300 =900 to represent, p, in dollars for each bracelet and ,n, for the number of bracelets she needs to sell to make 900 dollars in profit. She knows she can make at most 200 bracelets from her materials. At least how much should she charge for each bracelet?

Question

Samantha makes unique bracelets. For a pack of materials she spends 300 dollars and hopes to make 900 dollars in profit. She writes the inequality Pn-300 =900 to represent, p, in dollars for each bracelet and ,n, for the number of bracelets she needs to sell to make 900 dollars in profit. She knows she can make at most 200 bracelets from her materials. At least how much should she charge for each bracelet?
A. 
atleast 4 dollars
B. 
atleast 6 dollars
C. 
atleast 3 dollars
D. 
atleast 2 dollars

GPT-4o mini · Answer

To find out how much Samantha should charge for each bracelet while ensuring she has a profit of at least 900 dollars, we can start with the equation she provided:

\[ Pn - 300 = 900 \]

Here, $ P $ is the price per bracelet, and $ n $ is the number of bracelets she sells. Rearranging the inequality gives:

\[ Pn = 900 + 300 \]
\[ Pn = 1200 \]
\[ P = \frac{1200}{n} \]

Since she can make at most 200 bracelets, we have $ n \leq 200 $. To find the minimum price per bracelet, we need to consider the maximum number of bracelets she can sell, which is 200.

Now, substituting $ n = 200 $ into the equation for $ P $:

\[ P = \frac{1200}{200} = 6 \]

To ensure she meets her profit goal of 900 dollars, Samantha must charge at least $6 per bracelet when she sells 200 bracelets.

Thus, the answer is:

B. at least 6 dollars.