Question

Kelsey must pay $200 to rent a booth at the craft fair. The materials for each pendant cost $7.80, and she plans to sell each pendant for $13.50. To make a profit, she must make more money than she spends. Kelsey has already made 10 pendants. Part A Given that Kelsey has already made 10 pendants, how many additional pendants must she make and sell to make a profit of $50? More pendants to make a $50 profit

Answer 1

Kelsey must sell at least 34 additional pendants at $13.50 each to cover her initial costs and make a $50 profit, considering the $7.80 cost to make each pendant and the $200 booth rental fee.

Step-by-step explanation:

To calculate how many additional pendants Kelsey needs to sell to make a profit of $50 after accounting for the initial booth cost of $200 and the cost to make each pendant, we can set up an equation. First, we determine the net profit per pendant, which is the selling price minus the cost to make the pendant: $13.50 - $7.80 = $5.70 per pendant. She needs to cover the booth rental cost and make an additional $50 in profit. Kelsey has already made 10 pendants, so she has covered $57 (10 pendants × $5.70) of the $200 booth rental fee.

Now, we calculate the total profit needed, including the $50 desired profit and the remaining booth cost:
Total profit needed = $200 (booth cost) - $57 (10 pendants already made) + $50 (desired profit) = $193.

Then, we divide the total profit needed by the net profit per pendant to find how many additional pendants must be sold:
$193 ÷ $5.70 = 33.86. Since Kelsey cannot sell a fraction of a pendant, she must make and sell at least 34 additional pendants to achieve her profit goal of $50.