Calculating The Cost Per Cavity Filling Anja's Dental Expenses

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Anja's recent trip to the dentist resulted in a total bill of $628.35. This comprehensive cost encompassed a flat fee of $89.95 for the routine checkup and cleaning, along with the expense of filling four cavities. Each cavity filling incurred an equal cost, which we aim to determine through a precise equation and calculation. In this article, we will delve into the mathematical representation of Anja's dental expenses, unraveling the equation that unveils the individual cost of each cavity filling. Our focus will be on understanding the interplay between the flat fee, the total cost, and the number of cavities filled, ultimately leading us to the solution for the unknown variable, the cost per cavity.

Deconstructing Anja's Dental Bill: A Step-by-Step Analysis

To effectively dissect Anja's dental bill, we must first identify the key components that contribute to the total cost. The initial flat fee of $89.95 covers the fundamental services of a checkup and cleaning, forming the base of the overall expense. Subsequently, the cost of filling the four cavities adds to the total, with each filling incurring an identical charge. To determine the cost per cavity, we need to isolate this variable and formulate an equation that accurately represents the relationship between the known quantities and the unknown cost. This process involves subtracting the flat fee from the total bill, leaving us with the aggregate cost of the cavity fillings. Subsequently, dividing this aggregate cost by the number of cavities filled will reveal the individual cost per cavity. By meticulously following these steps, we can systematically unravel the financial aspects of Anja's dental visit and arrive at a precise understanding of the cost associated with each cavity filling. This step-by-step analysis will not only provide a numerical answer but also enhance our comprehension of the underlying mathematical principles governing such financial scenarios.

Formulating the Equation: Representing the Cost per Cavity

In order to determine the precise cost per cavity, we must construct an equation that encapsulates the relationship between the known values and the unknown variable, which we will denote as 'xx'. The total cost of Anja's dental visit, $628.35, is the sum of the flat fee for the checkup and cleaning ($89.95) and the cost of filling the four cavities (4 * xx). This relationship can be mathematically represented by the following equation:

$628.35 = $89.95 + 4x

This equation serves as the foundation for our calculation, providing a clear and concise representation of the financial components involved in Anja's dental expenses. The left-hand side of the equation signifies the total cost, while the right-hand side breaks down the cost into its constituent parts: the flat fee and the cost of the cavity fillings. By carefully analyzing this equation, we can isolate the variable 'xx' and determine the cost per cavity. The accurate formulation of this equation is crucial for obtaining a reliable solution and understanding the financial implications of Anja's dental treatment.

Solving for 'x': Unveiling the Cost per Cavity

With the equation $628.35 = 89.95+4xestablished,wecannowproceedtosolvefor′89.95 + 4x established, we can now proceed to solve for 'x′,thecostpercavity.Toisolate′', the cost per cavity. To isolate 'x

, we must first subtract the flat fee ($89.95) from both sides of the equation:

$628.35 - $89.95 = 4x

This simplifies to:

$538.40 = 4x

Next, to determine the value of 'xx', we divide both sides of the equation by 4:

$538.40 / 4 = x

This calculation yields:

$x = $134.60

Therefore, the cost of each cavity filling is $134.60. This step-by-step solution demonstrates the methodical approach required to solve algebraic equations and extract meaningful information from real-world scenarios. By carefully isolating the variable of interest, we can accurately determine the unknown cost and gain a deeper understanding of the financial aspects of Anja's dental treatment.

Verifying the Solution: Ensuring Accuracy and Reliability

To ensure the accuracy and reliability of our solution, it is crucial to verify the calculated cost per cavity by substituting it back into the original equation. This process involves plugging the value of 'xx' ($134.60) back into the equation $628.35 = $89.95 + 4x and confirming that the equation holds true.

Substituting $x = $134.60, we get:

$628.35 = $89.95 + 4($134.60)

Simplifying the equation:

$628.35 = $89.95 + $538.40

$628.35 = $628.35

The equation holds true, confirming that our calculated cost per cavity of $134.60 is indeed accurate. This verification step is essential in ensuring the correctness of our solution and providing confidence in our understanding of the problem. By meticulously checking our work, we can avoid errors and ensure that our conclusions are well-supported by the evidence. This verification process is a fundamental aspect of mathematical problem-solving and critical thinking.

Conclusion: The Cost of a Healthy Smile

In conclusion, by carefully analyzing Anja's dental bill and applying algebraic principles, we have successfully determined the cost per cavity filling. The equation $628.35 = 89.95+4xaccuratelyrepresentsthefinancialcomponentsofAnja′sdentalexpenses,allowingustosolvefortheunknownvariable′89.95 + 4x accurately represents the financial components of Anja's dental expenses, allowing us to solve for the unknown variable 'x

. Through a step-by-step solution, we found that each cavity filling cost 134.60.Thissolutionwasverifiedbysubstitutingthevalueof′134.60. This solution was verified by substituting the value of 'x
back into the original equation, confirming its accuracy and reliability.

This exercise demonstrates the practical application of mathematical concepts in real-world scenarios. By understanding the relationship between costs, fees, and quantities, we can effectively analyze financial information and make informed decisions. The cost of a healthy smile extends beyond the monetary value, encompassing the importance of preventive care and timely treatment. By addressing dental issues promptly, individuals can maintain their oral health and avoid more extensive and costly procedures in the future.

Keywords: dental cost, cavity filling cost, equation solving, algebraic principles, financial analysis