A mixture of 125 gallons of wine and water contains 20% water.How much water must be added.to the mixture in order to increase the precentage of water to 25% of the new mixture ?

Options

A. 8gals
B. 8.5gals
C. 10gals
D. 8.33gals

Answer

To solve the problem step by step, we need to determine how much water must be added to a mixture of wine and water to increase the percentage of water from 20% to 25%.

### Step 1: Calculate the amount of water in the initial mixture.
The initial mixture is 125 gallons, and it contains 20% water.

\[ \text{Amount of water} = 20\% \text{ of } 125 \text{ gallons} = \frac{20}{100} \times 125 = 25 \text{ gallons} \]

### Step 2: Calculate the amount of wine in the initial mixture.
The remaining part of the mixture is wine.

\[ \text{Amount of wine} = 125 \text{ gallons} - 25 \text{ gallons} = 100 \text{ gallons} \]

### Step 3: Set up the equation for the new mixture.
Let \( x \) be the amount of water to be added. After adding \( x \) gallons of water, the total amount of water in the mixture will be:

\[ \text{New amount of water} = 25 + x \text{ gallons} \]

The total volume of the new mixture will be:

\[ \text{Total volume} = 125 + x \text{ gallons} \]

### Step 4: Set up the equation to find \( x \).
We want the percentage of water in the new mixture to be 25%. Therefore, we can set up the following equation:

\[ \frac{25 + x}{125 + x} = 25\% \]

Converting 25% to a fraction gives us:

\[ \frac{25 + x}{125 + x} = \frac{25}{100} \]

### Step 5: Cross-multiply to solve for \( x \).
Cross-multiplying gives us:

\[ 100(25 + x) = 25(125 + x) \]

Expanding both sides:

\[ 2500 + 100x = 3125 + 25x \]

### Step 6: Rearranging the equation.
Now, we need to isolate \( x \):

\[ 100x - 25x = 3125 - 2500 \]

\[ 75x = 625 \]

### Step 7: Solve for \( x \).
Now, divide both sides by 75:

\[ x = \frac{625}{75} = \frac{125}{15} \approx 8.33 \text{ gallons} \]

### Conclusion:
To increase the percentage of water in the mixture to 25%, approximately 8.33 gallons of water must be added.

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