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Which equation would help determine the cost of 2 rubber stamps? Choose 1 answer: (A) \( \frac{2}{x}=\frac{\$ 10.30}{10} \) (B) \( \frac{x}{2}=\frac{10}{\$ 10.30} \) (C) \( \frac{2}{10}=\frac{\$ 10.30}{x} \) (D) \( \frac{2}{\$ 10.30}=\frac{x}{10} \)

Ask by Perkins Adkins. in the United States
Jan 24,2025

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Answer

The correct equation is \( \frac{x}{2} = \frac{10}{\$10.30} \), which is option B.

Solution

To determine the cost of **2 rubber stamps**, let's analyze the given options and identify which equation correctly sets up the relationship between the number of stamps and their cost. ### Given: - **10 stamps cost \$10.30** Let: - **\( x \)** be the cost of **2 stamps**. ### Proportional Relationship: Since the cost is directly proportional to the number of stamps, we can set up the proportion as: \[ \frac{\text{Cost of 2 stamps}}{\text{Number of stamps}} = \frac{\text{Cost of 10 stamps}}{\text{Number of stamps}} \] \[ \frac{x}{2} = \frac{10.30}{10} \] This simplifies to: \[ \frac{x}{2} = \frac{10}{10.30} \] ### Matching the Options: - **Option (B)** exactly matches this setup: \[ \frac{x}{2} = \frac{10}{\$10.30} \] ### Solving for \( x \): \[ x = 2 \times \frac{10}{10.30} \approx \$1.94 \] Therefore, **Option (B)** correctly represents the equation needed to determine the cost of 2 rubber stamps. **Answer:** **\(\boxed{\text{B}}\)**

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To determine the cost of 2 rubber stamps, you can set up a proportion based on the cost of 10 stamps. If 10 stamps cost \$10.30, you can find the amount for 2 stamps by calculating it proportionately. For instance, using choice (C) \( \frac{2}{10}=\frac{\$ 10.30}{x} \) allows you to solve for \( x \), the cost of 2 stamps. When approaching proportion problems like this, avoid common mistakes like incorrectly setting up your ratios. Ensure that the quantities you compare (like the number of stamps to their costs) match correctly to get an accurate result. Using proper cross-multiplication will save you from a lot of headaches!

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