Solving Tabitha's Medical Costs: An Equation Guide

Hey everyone, let's break down this math problem together! We're diving into a scenario with Tabitha and her medical expenses. The goal? To understand which equation correctly represents her costs. This isn't just about finding the right answer; it's about learning how to translate a real-life situation into a mathematical equation. It's super practical, trust me! This skills helps you in finance problems, and in the real world. So, grab your pencils and let's get started.

Understanding the Problem: Tabitha's Expenses

Alright, let's get down to the nitty-gritty of Tabitha's situation. The problem states that Tabitha pays a $20 co-pay for her doctor's visit. That's a flat fee, meaning it's a one-time cost. Additionally, she pays $10 for each prescription she gets. We're also told that her total expenses for the doctor and any prescriptions amounted to $50. The key here is to identify the fixed and variable costs. The co-pay is fixed; it's the same regardless of how many prescriptions she has. The prescription cost, however, varies depending on the number of prescriptions. Each prescription adds another $10 to the total cost. Let's make sure we've got all the facts straight before we start looking at the answer options, okay? The fixed cost is the doctor's visit, and the variable is each prescription, which is charged by how many prescriptions she gets. Remember that, it's very important to set up the equation.

Breaking Down the Costs

To make things super clear, let's list out what we know. First, there's the doctor's visit, which costs $20. This is a one-time charge. Then, there's the prescription cost: $10 per prescription. The total spent by Tabitha is $50. Now, how do we turn this into math? We need to use variables to represent unknown quantities, such as the number of prescriptions Tabitha got. Let's define our variables, shall we? Let 'x' represent the number of prescriptions. The cost for the prescriptions, therefore, will be $10 times 'x', or 10x. This will vary depending on how many prescriptions she has. The total expense will be the sum of fixed and variable costs. Fixed costs are the same in all cases. In the case of this problem, it is $20. Variable costs are dependent on how many prescriptions Tabitha gets. The variable cost is $10 per prescription, and the number of prescriptions is x. This translates to $10x. So, in total, it is $10x + $20, which is equal to $50. Now, with a clear understanding of the situation and all the factors in consideration, let us begin.

Analyzing the Answer Options

Okay, team, time to examine the options and figure out which one fits the bill. We're looking for an equation that accurately reflects Tabitha's costs. Remember, a correct equation will include the fixed cost for the doctor's visit and the variable cost for the prescriptions. Let's look at each option one by one, and then we will select the most suitable answer.

Option A: $10x = 50

This equation is pretty straightforward. It says that 10 times the number of prescriptions equals $50. Where's the doctor's visit co-pay? This equation completely ignores the initial $20 cost for the visit. This is a big red flag! Because of this, this option is not correct, because it does not consider the $20 copay, and the equation should equate to the total cost ($50). This equation might represent a scenario where each prescription costs $5, but not in Tabitha's case. Therefore, option A is wrong.

Option B: $20x + 10 = 50

This option suggests that $20 times the number of prescriptions, plus $10, equals $50. Hmm, is this right? The $20 doesn't represent the co-pay, but the multiplication by x suggests that it is a variable cost per prescription, but that's incorrect. The doctor's visit cost is fixed, so this equation misrepresents the fixed and variable costs. Because of this misrepresentation, option B is wrong. Additionally, the prescription cost is $10 per prescription, and the equation should reflect that, but this option does not. So, this option is not correct.

Option C: $10x + 20 = 50

Alright, let's take a closer look at this one. This equation starts with $10x. As we've discussed, 'x' represents the number of prescriptions, and each prescription costs $10. So, $10x accurately reflects the variable cost. Then, it adds $20. Remember the fixed cost? Yes, the doctor's visit! This equation correctly adds the $20 for the visit. Finally, the equation sets this sum equal to $50, which is the total cost. This is looking promising, guys! Everything adds up, literally and figuratively, making this option a strong contender. The $10x represents the variable cost per prescription, and the $20 represents the doctor's visit. The whole equation equates to $50, which is Tabitha's total expenses. So, option C is the most probable one, as it satisfies all the conditions of the problem.

Option D: $3x + 20 = 50

Now, let's break down this option. The equation includes $3x, which implies a cost of $3 per prescription. However, we know that each prescription costs $10, not $3. Because of this, the equation misrepresents the prescription cost, so this option is incorrect. The $20 represents the doctor's visit, which is a fixed cost, which is correct. But, as we mentioned, the prescription cost should be $10 per prescription. Since this equation is not reflecting the prescription cost, it is incorrect. The total expenses are also $50, but because the prescription cost is wrong, the whole equation is not correct.

The Correct Equation

Alright, drumroll, please! The correct equation is C: $10x + 20 = 50. This equation perfectly captures Tabitha's medical expenses: the $10 per prescription multiplied by the number of prescriptions (x), plus the $20 co-pay, totaling $50. This equation is complete and accurate, representing the scenario described in the problem. The most important thing here is to understand how the components are reflected and the relationship of the numbers. After that, it is easy to find the correct answer.

Key Takeaways and Tips for Similar Problems

So, what have we learned, guys? Here's the gist of it:

• Identify the Fixed and Variable Costs: This is the first step! Know what's a one-time cost (like the doctor's visit) and what changes based on the situation (like the prescriptions).
• Use Variables Correctly: 'x' (or any letter) is your friend! It represents the unknown quantity. Make sure you know what each variable represents in your equation.
• Translate Words to Math: Break down the problem, and translate each sentence into a mathematical expression. The word 'per' usually means multiplication.
• Check Your Work: Always review your equation to make sure it makes sense in the context of the problem. Does it account for all the costs? Does it seem logical?

Keep practicing! The more problems you solve, the better you'll become at translating real-world situations into mathematical equations. You've got this!