A fashion designer makes and sells hats. The material for each hat costs $5.50. The hats sell for $12.50 each. The designer spends $1400 on advertising. How many hats must the desi... A fashion designer makes and sells hats. The material for each hat costs $5.50. The hats sell for $12.50 each. The designer spends $1400 on advertising. How many hats must the designer sell to break even?
Understand the Problem
The question asks us to determine the number of hats a fashion designer needs to sell in order to cover all expenses, including the cost of materials and advertising, to break even. This problem requires us to calculate the profit per hat (selling price minus material cost) and then determine how many hats need to be sold at that profit margin to cover the advertising expenses.
Answer
The designer must sell 200 hats to break even.
Answer for screen readers
The designer must sell 200 hats to break even.
Steps to Solve
- Calculate the profit per hat
To find the profit per hat, subtract the cost of the materials from the selling price:
$Profit = Selling\ Price - Material\ Cost$ $Profit = $12.50 - $5.50 = $7.00$
- Determine the number of hats to sell to break even
To break even, the total profit from selling hats must equal the advertising expenses. Divide the total advertising cost by the profit per hat to find the number of hats that need to be sold:
$Number\ of\ hats = \frac{Advertising\ Expenses}{Profit\ per\ hat}$ $Number\ of\ hats = \frac{$1400}{$7.00} = 200$
The designer must sell 200 hats to break even.
More Information
Breaking even means that the total revenue equals total expenses. In this scenario, the total amount earned from selling the hats must be equal to the amount spent on the material and advertising
Tips
A common mistake is to forget to calculate the profit per hat first or to incorrectly subtract the cost of materials from the selling price. Another mistake is to divide the profit per hat by the advertising expenses instead of the other way around.
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