Problem 20 - Algebra and Trigonometry

Question

The selling price of a scientific calculator is \(\$ 15 .\) If the markup is \(25 \%\) of the dealer's cost, what is the dealer's cost of the calculator?

Step-by-Step Solution

Answer

The dealer's cost price for the scientific calculator is \$12.

Step 1: Understanding the problem

We need to find the dealer's cost price. We know that the selling price for the calculator is \$15 and the markup is 25% of the dealer's cost (i.e the cost price). This markup price is the difference between the selling price and the cost price.

Step 2: Setup the equation

Based on the problem, we can set up the equation as follows: selling price = cost price + markup. We can express this equation in terms of 'p' where p is the cost price. Therefore, the equation becomes: \$15 = p + 0.25p.

Step 3: Simplify the equation

The term 0.25p means 25% of p (which is the markup). When we combine p and 0.25p, it becomes 1.25p. So, the equation becomes: \$15 = 1.25p.

Step 4: Solve for p

To get the cost price p, we divide both sides of the equation by 1.25. This results in: p = \$15 / 1.25.

Step 5: Compute the cost price

Carry out the division to get the dealer's cost price. p = \$12.

Key Concepts

Selling Price

The selling price is the amount a customer pays for a product or service. In this exercise, the selling price of the scientific calculator is clearly given as $15. Understanding the selling price is essential, as it includes both the cost of the item to the dealer and the markup percentage that allows the dealer to earn profit.

The selling price is a critical part of retail business since it directly affects both consumer purchase decisions and dealer profitability.

• It encapsulates the total value attributed to the product after all cost and profit margins are considered.
• In a marketplace, a competitive selling price can attract more customers.

When solving related problems, knowing the selling price helps you derive other important values like the cost price or the markup.

Dealer's Cost

The dealer's cost, or cost price, is the amount a dealer pays to acquire a product before selling it to customers. It's the baseline price before any markups are added.

In this exercise, the calculation of the dealer's cost is necessary to understand how markups work in forming the final selling price. When a product is marked up, it simply means that an additional percentage over the dealer's cost is added to arrive at the selling price.

• The dealer's cost can be calculated if the selling price and markup percentage are known—like in this exercise.
• This cost needs to be kept as low as possible for retailers to sustain competitive pricing.

If a dealer knows the cost accurately, they can strategically set prices that optimize both profit and customer relations.

Markup Percentage

Markup percentage is essentially the difference between the selling price and the cost price, expressed as a percentage of the cost price. It represents the additional percentage over the cost price that creates profit.

For our calculator, the markup percentage is given as 25%. This means the selling price includes an additional 25% over what it cost the dealer to purchase the calculator.

• Understanding markup percentage is critical for assessing profitability.
• Higher markup percentages lead to higher profits but could risk lowering sales if the price appears too high.

Knowing the markup percentage allows dealers to make informed pricing strategies while balancing profit-making and competitiveness.

Cost Equation

The cost equation is a mathematical formula that helps determine various financial variables in a transaction, such as cost price, selling price, and markup. It is the relationship expressed as:

\[ \text{Selling Price} = \text{Cost Price} + \text{Markup Value} \]
In our scenario, this translates to:

\[ 15 = p + 0.25p \]
Where \( p \) is the dealer's cost (cost price).

The simplified version of our equation becomes:

\[ 15 = 1.25p \]
This equation is instrumental in isolating the cost price, \( p \), which can be achieved by dividing the selling price by \( 1.25 \) to yield the cost price.

• Cost equations help in organizing financial calculations logically.
• They are vital in business for setting adequate prices and understanding cost structures thoroughly.

Properly using cost equations will ensure accurate computation of values critical for any retail business operation.