Mason makes specialty cards. For a pack of materials he spends 600 dollars and hopes to make 800 dollars in profit. He writes the inequality Pn-600 =800 to represent, p, in dollars for each bracelet and ,n, for the number of bracelets she needs to sell to make 800 dollars in profit. He knows he can make at most 700 bracelets from his materials. At least how much should she charge for each bracelet?

Question

A.
2 dollars
B.
1 dollar
C.
1.50 dollars
D.
3 dollars

Answer 1

To solve the problem, we first need to set up the correct inequality based on the information provided.

Mason spends $600 for materials and wants to make a profit of $800. Therefore, his total revenue from selling \( n \) bracelets priced at \( p \) dollars each should cover both his expenses and the desired profit.

The inequality can be expressed as:

\[ Pn - 600 \geq 800 \]

This simplifies to:

\[ Pn \geq 1400 \]

Now, we also know that Mason can make at most 700 bracelets. Therefore, \( n \) can be at most 700. Thus, we can substitute 700 for \( n \):

\[ P(700) \geq 1400 \]

Now we can solve for \( P \):

\[ 700P \geq 1400 \]

Dividing both sides by 700 gives:

\[ P \geq \frac{1400}{700} \]

\[ P \geq 2 \]

This means Mason should charge at least $2 for each bracelet.

So the answer is:

A. 2 dollars