Problem 31 - Elementary Algebra

Question

Set up an equation and solve each problem. (Objectives 2 and 3) A retailer has some toe rings that cost him \(\$ 5\) each. He wants to sell them at a profit of \(70 \%\) of the cost. What should the selling price be for the toe rings?

Step-by-Step Solution

Answer

The selling price should be $8.50.

Step 1: Understand the Profit Requirement

The retailer wants to sell the toe rings at a profit of 70% of the cost. This means the selling price should be the cost plus this 70% profit.

Step 2: Express the Profit Mathematically

To find the 70% profit, calculate 70% of the cost price of each toe ring. Use the formula for percentage calculation: Profit = Percentage × Cost. Here, Profit = 0.70 × $5 = $3.50.

Step 3: Calculate the Selling Price

Add the profit to the original cost to get the selling price. Selling Price = Cost + Profit. Therefore, Selling Price = $5 + $3.50 = $8.50.

Key Concepts

Profit Calculation

When a retailer sells an item, such as a toe ring, they often want to make a profit. Profit is essentially the amount of money made over the initial cost of the item. In our situation, the toe rings cost the retailer \(5 each. He aims to make a 70% profit.
- To find out how much money that represents, calculate 70% of the cost. This is done using the formula:\[\text{Profit} = \text{Percentage} \times \text{Cost}\]In this exercise, the profit can be calculated as:\[0.70 \times 5 = 3.50\]So, the profit from selling one toe ring is \)3.50. This profit is then added to the cost to form the selling price.

Percentage Increase

Understanding percentage increase is crucial to figuring out profit margins. A percentage increase shows how much a value grows as a percentage of its original value. When talking about profits, this indicates the additional percentage of the cost price you aim to earn.
- In this context, calculate a 70% increase over the initial cost of $5.
Multiplying $5 by 0.70 gives us the increase amount of $3.50. When we combine this with the original price, you find the new price, which in this case, is the amount customers are asked to pay.

Cost and Selling Price

Determining the selling price is a straightforward process if you understand the relationship between cost and profit. The cost is simply the amount paid to acquire each toe ring, which is \(5. The selling price is the amount a customer should pay, covering both the initial cost and the desired profit.
- To get the selling price, add the profit to the original cost.
Here's the equation:\[\text{Selling Price} = \text{Cost} + \text{Profit}\]So, adding a \)3.50 profit to the \(5 cost results in a selling price of \)8.50.
This way, the retailer adequately covers his costs and achieves the intended profit of 70%.