Determining Electric Scooter Cost Expression From Total Cost And Helmet Price

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In the realm of mathematics, we often encounter scenarios that require us to decipher relationships between variables and constants. This exploration delves into one such scenario, where we aim to determine the cost of an electric scooter given the combined cost of the scooter and a helmet, along with the individual cost of the helmet. This problem exemplifies the application of algebraic principles to solve real-world problems, highlighting the importance of mathematical reasoning in everyday situations. Let's embark on this mathematical journey to unravel the cost of the electric scooter.

Before we delve into the solution, it's crucial to dissect the problem statement and identify the key information provided. We are given that the combined cost of a new electric scooter and a helmet is represented by the variable C. This signifies that C encompasses the total expenditure incurred for both items. Additionally, we know that the cost of the helmet alone is $142. This provides us with a concrete numerical value that we can utilize in our calculations. Our objective is to determine an expression that represents the cost of the electric scooter exclusively, excluding the helmet's price. This requires us to isolate the scooter's cost from the combined cost, effectively separating the two components.

To arrive at the expression that represents the cost of the electric scooter, we need to employ algebraic principles. We know that the combined cost (C) is the sum of the scooter's cost and the helmet's cost. Let's denote the cost of the electric scooter as S. Therefore, we can express the relationship as follows:

C = S + $142

Our goal is to isolate S, which represents the scooter's cost. To achieve this, we need to subtract the helmet's cost ($142) from both sides of the equation. This maintains the equality while effectively isolating S on one side.

C - $142 = S + $142 - $142

Simplifying the equation, we get:

C - $142 = S

Therefore, the expression that represents the cost of the electric scooter is C - $142. This expression signifies that the scooter's cost is equal to the combined cost minus the helmet's cost.

Now that we have derived the expression for the scooter's cost, let's evaluate the options provided to identify the correct one.

  • A. C + $142: This expression represents the combined cost plus the helmet's cost, which is not what we are looking for. It would result in a value greater than the combined cost, which is incorrect.
  • B. C × $142: This expression represents the combined cost multiplied by the helmet's cost, which has no logical connection to the scooter's cost. It would yield a significantly larger value, which is not relevant to the problem.
  • C. $142 - C: This expression represents the helmet's cost minus the combined cost, which would result in a negative value. This is not a feasible representation of the scooter's cost, as costs cannot be negative.
  • D. C - $142: This expression matches the expression we derived for the scooter's cost, which is the combined cost minus the helmet's cost. This is the correct option.

Therefore, the correct expression that represents the cost of just the electric scooter is D. C - $142.

This mathematical problem has practical implications in real-life scenarios. Imagine you are purchasing an electric scooter and a helmet. The store offers a package deal where the combined cost is C. If you already know the helmet's price is $142, you can use the expression C - $142 to determine the actual cost of the scooter. This allows you to make informed decisions about your purchase and budget accordingly.

Moreover, this problem highlights the importance of breaking down complex scenarios into smaller, manageable components. By isolating the known variables and applying basic algebraic principles, we can solve for the unknown, gaining a clearer understanding of the situation.

In conclusion, the expression that represents the cost of just the electric scooter is C - $142. This solution is derived by understanding the relationship between the combined cost, the helmet's cost, and the scooter's cost, and then applying algebraic principles to isolate the scooter's cost. This problem showcases the practical application of mathematics in everyday scenarios, emphasizing the importance of mathematical reasoning and problem-solving skills. By dissecting the problem, formulating an equation, and evaluating the options, we successfully determined the expression that accurately represents the cost of the electric scooter.

This exercise not only provides a solution to a specific problem but also reinforces the broader concept of using mathematical tools to analyze and understand real-world situations. The ability to translate word problems into mathematical expressions and solve them is a valuable skill that extends far beyond the classroom, empowering individuals to make informed decisions and navigate the complexities of life.