Problem 32 - Elementary Algebra

Question

Set up an equation and solve each problem. (Objectives 2 and 3) A retailer has some video games that cost her \(\$ 25\) each. She wants to sell them at a profit of \(80 \%\) of the cost. What price should she charge for the video games?

Step-by-Step Solution

Answer

The retailer should charge $45 per video game.

Step 1: Determine the Profit

First, calculate the profit using the given percentage. Since the profit is 80% of the cost, multiply the cost by 0.80. So, profit = 25 * 0.80 = 20.

Step 2: Calculate the Selling Price

To find out the selling price, add the profit to the original cost of the video game. The cost of each game is $25 and the profit is $20. So, selling price = 25 + 20 = 45.

Key Concepts

Profit Calculation

Calculating profit is a fundamental aspect of elementary algebra and is essential when it comes to understanding how businesses determine their selling prices. In this scenario, we start by identifying the cost price of the video games, which is given as $25 each. The retailer aims to make a profit of 80% on this cost. To determine the profit, we multiply the cost price by the percentage profit, expressed as a decimal. For an 80% profit, this is equivalent to a multiplication factor of 0.80. Therefore, the profit per video game is calculated as follows:

• Profit = Cost Price × Percentage Profit
• Profit = 25 × 0.80
• Profit = $20

Hence, the profit on each video game amounts to $20, which will later be added to the original cost to find the selling price.

Equation Setup

Setting up an equation allows us to clearly and methodically solve for the desired value. In this exercise, the focus is on finding the selling price by using simple algebraic expressions. Begin with the given data:

• Cost Price of a video game = \(25
• Desired Profit = 80% of the Cost Price

Using these values, we express the profit as a part of the equation:\( \text{Selling Price} = \text{Cost Price} + \text{Profit} \)Substituting the given values into the equation allows us to solve for the selling price:

• Selling Price = \)25 + (\(25 × 0.80)
• Selling Price = \)25 + \(20
• Selling Price = \)45

Thus, by setting up this equation, it becomes straightforward to solve for the selling price efficiently.

Percentage Profit

Understanding percentage profit is key in calculations related to pricing and revenue in numerous business applications. In simple terms, it is the percentage of the cost that you wish to earn in addition to the original price. To express a percentage as a decimal, simply divide by 100. For example, an 80% profit is equivalent to a decimal of 0.80. This conversion is crucial for calculations in algebra. In our exercise, this allowed us to effectively calculate the profit that corresponds to 80% of the $25 cost price. Knowing this principle, we calculate:

• Decimal equivalent = 80% = 0.80
• Profit in dollars = Cost Price × Decimal equivalent
• Profit = $25 × 0.80 = $20

Thus, percentage profit helps to convert percentage intentions into tangible profit figures, essential for setting appropriate selling prices.