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Let's solve the problem step by step: --- **Step 1: Understand what 9.25% (v/v) means** - **9.25% (v/v)** means there are **9.25 mL of ethanol in every 100 mL of beer**. --- **Step 2: Set up a proportion to find the volume of beer containing 17 mL ethanol** Let \( V \) be the volume of beer (in mL) that contains 17 mL of ethanol. \[ \frac{9.25~\text{mL ethanol}}{100~\text{mL beer}} = \frac{17~\text{mL ethanol}}{V~\text{mL beer}} \] --- **Step 3: Solve for \( V \)** \[ \frac{9.25}{100} = \frac{17}{V} \] Cross-multiply: \[ 9.25 \times V = 17 \times 100 \] \[ 9.25V = 1700 \] \[ V = \frac{1700}{9.25} \] \[ V \approx 183.78~\text{mL} \] --- ### **Final Answer** **About 183.8 mL of the beer contains 17 mL of ethanol.** --- #### **Explanations:** - **Step 1:** Defined what percentage by volume means in this context. - **Step 2:** Set up a proportion based on the definition. - **Step 3:** Solved the proportion algebraically for the unknown volume.

The concept used involves understanding percentage volume/volume (% v/v) to relate the amount of ethanol to the total volume of beer. By setting up a proportional relationship between the known ethanol concentration and the unknown total volume, we can calculate how much beer contains a specific volume of ethanol. This relies on the principle that the ratio of ethanol volume to total beer volume remains constant at the given concentration.

The concept used in solving this problem centers around understanding and applying the meaning of percentage volume/volume (% v/v). This measure indicates the volume of ethanol present per unit volume of the entire beverage. Specifically, a 9.25% (v/v) beer contains 9.25 mL of ethanol in every 100 mL of beer. To determine how much beer contains a certain volume of ethanol—in this case, 17 mL—we set up a proportion based on the known concentration. By expressing the relationship as a ratio of ethanol volume to total beer volume, we can solve for the unknown volume of beer that would contain 17 mL of ethanol. This approach relies on the principle that the ratio of ethanol to total volume remains constant at the specified concentration, allowing us to perform straightforward algebraic calculations to find the desired volume.