A bartender mixes 30 ml of Port Wine having 10% alcohol concetration and 50 mI of Merlot wine having 21% alcohol concentration . The bartender needs to make a cocktail having 18% alcohol concentration. What volume of Chardonnay wine having 23% concentration must he use so that the final mixture has 18% concentration ?

Options

A. 18 ml
B. 20 ml
C. 33 ml
D. 45 ml

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Define the variables
Let \( x \) be the volume of Chardonnay wine (in ml) that the bartender needs to add.

### Step 2: Calculate the total alcohol from each type of wine
1. **Port Wine**:
- Volume = 30 ml
- Alcohol concentration = 10%
- Alcohol from Port Wine = \( 30 \times \frac{10}{100} = 3 \) ml

2. **Merlot Wine**:
- Volume = 50 ml
- Alcohol concentration = 21%
- Alcohol from Merlot Wine = \( 50 \times \frac{21}{100} = 10.5 \) ml

3. **Chardonnay Wine**:
- Volume = \( x \) ml
- Alcohol concentration = 23%
- Alcohol from Chardonnay Wine = \( x \times \frac{23}{100} = 0.23x \) ml

### Step 3: Calculate the total volume of the mixture
The total volume of the mixture will be:
\[ 30 + 50 + x = 80 + x \text{ ml} \]

### Step 4: Set up the equation for the desired alcohol concentration
The bartender wants the final mixture to have an alcohol concentration of 18%. Therefore, the total alcohol in the mixture should equal 18% of the total volume:
\[ \text{Total Alcohol} = 3 + 10.5 + 0.23x \]
\[ \text{Total Volume} = 80 + x \]
Setting up the equation:
\[ 3 + 10.5 + 0.23x = 0.18(80 + x) \]

### Step 5: Simplify the equation
Combine the constants on the left side:
\[ 13.5 + 0.23x = 14.4 + 0.18x \]

### Step 6: Rearrange the equation
Move all terms involving \( x \) to one side and constant terms to the other:
\[ 0.23x - 0.18x = 14.4 - 13.5 \]
\[ 0.05x = 0.9 \]

### Step 7: Solve for \( x \)
Divide both sides by 0.05:
\[ x = \frac{0.9}{0.05} = 18 \]

### Conclusion
The volume of Chardonnay wine that the bartender must use is \( \boxed{18} \) ml.

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