If a head of lettuce costs a retailer 0.68, at what price...

If a head of lettuce costs a retailer $$\$ 0.68,$$ at what price should it be sold to yield a profit of $60 \%$ on the selling price?If a pair of shoes costs a retailer $$\$ 24,$$ and he sells them for $$\$ 39.60,$$ what is his rate of profit based on the cost?

Key Concepts

Selling Price Determination Based on Profit Margin

This concept involves finding the selling price when a specific profit margin is desired on that selling price. It requires setting up the equation where the cost is a known percentage of the selling price. For example, if the goal is to achieve a 60% profit margin based on the selling price, then the cost forms the remaining 40% of the selling price. This relationship enables one to solve for the selling price by dividing the cost by the decimal equivalent of that remaining percentage.

Profit Rate Computation Based on Cost

This concept refers to calculating the profit as a percentage relative to the cost price. It is computed using the formula: Profit Percentage equals (Selling Price minus Cost) divided by Cost, multiplied by 100. This calculation provides insight into how much profit is made in relation to the initial investment, serving as a measure of profitability for the seller.

Percentage to Decimal Conversion in Profit Calculations

Converting percentages to their decimal forms is fundamental in profit calculations because it facilitates the algebraic manipulation needed to solve equations involving percentages. Whether determining the selling price based on a desired profit margin or computing the profit rate from the cost, using the correct decimal representation of percentages ensures accurate and consistent results.

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