Serenity's Earnings Calculation How Many Articles Did She Write?

In this article, we delve into the financial world of Serenity, a dedicated journalist who contributes her writing skills to a website. Serenity's compensation structure is multifaceted, comprising a per-article payment and a weekly base salary. Understanding the interplay between these two components is crucial to deciphering her overall earnings. Serenity earns $42 for every article she crafts, reflecting the value placed on her individual contributions. This per-article payment serves as a direct incentive for Serenity to produce quality content consistently. In addition to the per-article earnings, Serenity also receives a weekly base salary of $160. This base salary provides a financial safety net, ensuring a minimum income regardless of the number of articles published in a given week. The combination of the per-article payment and the weekly base salary creates a dynamic earnings model for Serenity. Her total earnings are directly influenced by her productivity (number of articles written) while also providing a baseline income for financial stability. To analyze Serenity's earnings, we can represent her compensation structure using a mathematical equation. This equation will allow us to calculate her total earnings for any given week, based on the number of articles she writes. In Serenity's case, the equation representing her earnings last week is given as:

$42a + 160 = 622$

Where:

• $a$ represents the number of articles Serenity wrote during the week.

• $42$ represents the payment Serenity receives for each article.

• $160$ represents Serenity's weekly base salary.

• $622$ represents Serenity's total earnings for the week.

This equation forms the foundation for our analysis, enabling us to determine the number of articles Serenity wrote to achieve her total earnings of $622. In the subsequent sections, we will dissect this equation, employing algebraic principles to isolate the variable 'a' and ultimately solve for the number of articles Serenity contributed last week. This problem provides a practical application of linear equations, demonstrating how mathematical models can be used to represent real-world financial scenarios. By understanding the components of Serenity's earnings and applying algebraic techniques, we can gain valuable insights into her professional life and the relationship between her output and income.

Unveiling the Equation: A Step-by-Step Solution

Now, let's embark on a step-by-step journey to solve the equation and determine the number of articles Serenity wrote last week. Our primary goal is to isolate the variable '$a$' on one side of the equation. This will reveal the value of '$a$', which represents the number of articles. The given equation is:

$42a + 160 = 622$

The first step in solving for '$a$' is to isolate the term containing '$a$' (which is $42a$). To achieve this, we need to eliminate the constant term ($160$) from the left side of the equation. We can do this by subtracting $160$ from both sides of the equation. This ensures that the equation remains balanced, maintaining the equality between the two sides.

Subtracting $160$ from both sides, we get:

$42a + 160 - 160 = 622 - 160$

Simplifying the equation, we have:

$42a = 462$

Now, we have successfully isolated the term containing '$a$'. The next step is to isolate '$a$' itself. Since '$a$' is being multiplied by $42$, we need to perform the inverse operation, which is division. We will divide both sides of the equation by $42$ to isolate '$a$'.

Dividing both sides by $42$, we get:

$42a / 42 = 462 / 42$

Simplifying the equation, we have:

$a = 11$

Therefore, the solution to the equation is $a = 11$. This means that Serenity wrote $11$ articles last week to earn a total of $622.

We have successfully solved the equation using basic algebraic principles, demonstrating the power of mathematics in solving real-world problems. The step-by-step approach, involving subtraction and division, allowed us to systematically isolate the variable and arrive at the solution. This process highlights the importance of understanding the order of operations and the concept of inverse operations in equation solving. In the next section, we will verify our solution to ensure its accuracy and solidify our understanding of the problem.

Verifying the Solution: Ensuring Accuracy

To ensure the accuracy of our solution, it's crucial to verify that the value we obtained for '$a$' (which is $11$) satisfies the original equation. This verification process provides a check and balance, confirming that our calculations are correct and our solution is valid. We will substitute $a = 11$ back into the original equation:

$42a + 160 = 622$

Substituting $a = 11$, we get:

$42(11) + 160 = 622$

Now, we need to perform the calculations on the left side of the equation to see if it equals the right side.

First, we multiply $42$ by $11$:

$42 * 11 = 462$

Next, we add $160$ to the result:

$462 + 160 = 622$

So, the left side of the equation becomes:

$622 = 622$

As we can see, the left side of the equation equals the right side, which means our solution $a = 11$ is correct. This verification step confirms that Serenity indeed wrote $11$ articles last week to earn a total of $622. The verification process reinforces the importance of accuracy in problem-solving. By substituting the solution back into the original equation, we can identify any potential errors in our calculations and ensure that our answer is valid within the context of the problem. This practice is particularly valuable in mathematical problem-solving, where a single mistake can lead to an incorrect result. In the final section, we will summarize our findings and discuss the implications of Serenity's earnings structure.

Conclusion: Serenity's Journalistic Success

In conclusion, we have successfully navigated the mathematical landscape of Serenity's earnings as a journalist. By meticulously analyzing the provided equation and employing algebraic principles, we have determined the number of articles Serenity wrote last week. Our journey began with understanding Serenity's compensation structure, which comprises a per-article payment of $42 and a weekly base salary of $160. This combination of income sources provides both incentive for productivity and a baseline financial security.

We then translated this information into a mathematical equation:

$42a + 160 = 622$

Where '$a$' represents the number of articles written. Through a step-by-step solution process, involving subtraction and division, we isolated the variable '$a$' and arrived at the solution:

$a = 11$

This indicates that Serenity wrote $11$ articles last week. To ensure the accuracy of our solution, we performed a verification step, substituting $a = 11$ back into the original equation. The verification confirmed that our solution is correct, solidifying our understanding of the problem.

Serenity's earnings structure highlights the direct correlation between her output and income. By writing more articles, Serenity can increase her earnings, demonstrating the potential for financial growth within her profession. The base salary provides a stable foundation, while the per-article payment incentivizes productivity and rewards her writing efforts. This analysis of Serenity's earnings provides a practical application of mathematical principles in a real-world scenario. By understanding and manipulating equations, we can gain valuable insights into financial situations and make informed decisions. The problem also underscores the importance of journalists and their contributions to society. Serenity's dedication to her craft is reflected in her earnings, highlighting the value of quality journalism in today's world. This exploration of Serenity's earnings serves as a testament to the power of mathematics in understanding and interpreting the world around us. From personal finance to professional endeavors, mathematical principles provide a framework for analysis and decision-making, empowering us to navigate the complexities of life with confidence.