`{:("Column A" , "James purchased Medicine A for x dollars, which included a sales tax of 5%. Kate was charged 5% for sales tax on x dollars tha Medicine B costs ","ColumnB"),("Sales tax paid by James",,"Sales tax paid by Kate "):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem, we need to compare the sales tax paid by James and Kate based on the information given. Let's break down the solution step by step.

### Step 1: Understand the sales tax for James
James purchased Medicine A for \( x \) dollars, which includes a sales tax of 5%. We need to find the cost of the medicine before tax, denoted as \( c \).

The total cost \( x \) can be expressed as:
\[ x = c + \text{Sales Tax on } c \]
The sales tax on \( c \) is 5% of \( c \), which can be written as:
\[ \text{Sales Tax} = 0.05c \]
Thus, we can rewrite the equation as:
\[ x = c + 0.05c = 1.05c \]

### Step 2: Solve for \( c \)
From the equation \( x = 1.05c \), we can isolate \( c \):
\[ c = \frac{x}{1.05} \]

### Step 3: Calculate the sales tax paid by James
Now, we can find the sales tax paid by James:
\[ \text{Sales Tax paid by James} = 0.05c = 0.05 \left(\frac{x}{1.05}\right) \]
This simplifies to:
\[ \text{Sales Tax paid by James} = \frac{0.05x}{1.05} \]

### Step 4: Understand the sales tax for Kate
Kate was charged 5% for sales tax on the cost of Medicine B, which is \( x \) dollars. Therefore, the sales tax paid by Kate is:
\[ \text{Sales Tax paid by Kate} = 0.05x \]

### Step 5: Compare the sales tax paid by James and Kate
Now we have:
- Sales tax paid by James: \( \frac{0.05x}{1.05} \)
- Sales tax paid by Kate: \( 0.05x \)

To compare these two amounts, we can express them in a way that makes it easier to see which is larger.

### Step 6: Simplify the comparison
Let's compare:
\[ \frac{0.05x}{1.05} \quad \text{and} \quad 0.05x \]

We can rewrite the first term:
\[ \frac{0.05x}{1.05} = 0.05x \cdot \frac{1}{1.05} \]

Since \( \frac{1}{1.05} < 1 \), it follows that:
\[ \frac{0.05x}{1.05} < 0.05x \]

### Conclusion
From our calculations, we can conclude that the sales tax paid by Kate is greater than the sales tax paid by James. Therefore, Column B (sales tax paid by Kate) is larger than Column A (sales tax paid by James).

### Final Answer
The answer is that Column B is larger than Column A.

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