Question

Translate to an equation and solve. A writer earns \(15 \%\) of the publishing company's net profit on the sale of her book in royalties (commission). If the company sells \(13,000\) copies of the book and makes a profit of \(\$ 6\) on each book, what is the writer's royalty?

Short answer

Answer: The writer's royalty is $11,700.

Step-by-step solution

Calculate the total profit made by the publishing company

To find the total profit, multiply the number of books sold (13,000) by the profit made on each book (\(\$ 6\)). Total profit = Number of books sold × Profit on each book

Write the equation for the total profit

The equation for the total profit is: Total profit = 13,000 × 6

Solve the equation for the total profit

By solving the equation, we get the total profit made by the publishing company: Total profit = 13,000 × 6 = \$ 78,000

Write the equation for the writer's royalty

Since the writer earns \(15 \%\) of the net profit, the equation for the writer's royalty is: Writer's royalty = 15 \% × Total profit

Substitute the value of the total profit in the equation

Replace the total profit with the value calculated in step 3: Writer's royalty = 15 \% × \$ 78,000

Solve the equation for the writer's royalty

By solving the equation, we find the writer's royalty: Writer's royalty = 15 \% × \$ 78,000 = 0.15 × \$ 78,000 = \$ 11,700 The writer's royalty is \$ 11,700.

Key concepts

Percentage Calculation

Percentage calculation is a vital skill that allows us to understand how a quantity relates to a whole in the form of a fraction of 100. In the exercise, the writer's royalty is based on a percentage of the total profit. A percentage essentially tells us how many out of 100 parts of a whole something represents. For example, when we say 15%, it means 15 parts out of 100 parts of a particular value. To find a percentage amount, follow these steps:

• Convert the percentage to its decimal form by dividing it by 100. For instance, 15% becomes 0.15.
• Multiply the decimal with the total amount to find the percentage value. For example, to find 15% of $78,000, multiply 0.15 by $78,000, which equals $11,700.

Understanding this method is crucial when wanting to determine proportions, discounts, interests, or commissions from a total amount.

Profit and Loss

Profit and loss are essential concepts in financial mathematics, particularly in business where evaluating the outcomes of transactions is crucial. In the given problem, the profit earned by selling each book serves as the foundation for calculating the writer’s royalty. Profit is calculated when the selling price of a product is higher than its cost. Loss occurs when the selling price is lower than the cost. Here’s how you determine profit:

• Identify the selling price of an item.
• Subtract the cost price from the selling price.
• If the result is positive, it's a profit. If negative, it's a loss.

For instance, if each book sells for a profit of $6, then with 13,000 books sold, the total profit is $78,000. Calculating such profits helps in understanding the financial health and success of business activities.

Royalties

Royalties represent a form of payment to a property owner for the use of their intellectual property, such as a book, song, or invention. They are typically calculated as a percentage of the profit generated from the item being used, as seen in this writer's situation. The writer in the exercise earns royalties depending on the total sales profit, receiving 15% for each book sold. This is a common practice in creative and intellectual sectors, providing authors with passive income for each copy of their work sold. To calculate royalties:

• Determine the percentage of the profit agreed upon in the royalty contract.
• Multiply that percentage by the net profit amount for the total royalties the creator receives.

Royalties serve as a powerful motivator that can encourage creators by rewarding them financially when their works achieve commercial success.