sandra makes necklaces and sells them at a school craft fair. she uses the equation P=7.5cn-(2.25n+15) to determine her total profit at the fair when n neckleaces are sold. Based on this equation, how much does she charge for each necklace?

Question

A.$2.25
B.$7.50
C.$15.00
D.$17.25

Answer 1

To determine how much Sandra charges for each necklace, we can analyze the given profit equation:

\[ P = 7.5cn - (2.25n + 15) \]

Where:

• \( P \) = total profit,
• \( n \) = number of necklaces sold,
• \( c \) = cost per necklace.

From the equation, \( P \) can also be expressed as

\[ P = (price \cdot n) - (cost \cdot n + fixed costs) \]

Here, \( 7.5cn \) represents the total revenue from selling \( n \) necklaces at a price of \( 7.5 \). The term \( (2.25n + 15) \) represents the total costs, which consist of a variable cost of $2.25 per necklace \( (2.25n) \) and a fixed cost of $15.

To find how much Sandra charges for each necklace, we look at the coefficient of \( n \) in the revenue term.

The price per necklace (the revenue part) can be identified in the profit equation:

• Sales revenue per necklace = $7.50

Thus, the answer is:

B. $7.50