A mixture is made by combining a red liquid and a blue liquid so that the ratio of the red liquid to the blue liquid is 17 to 3 by weight. How many liters of the blue liquid are needed to make a 420 - liter mixture?

Answer

To solve the problem of how many liters of blue liquid are needed to make a 420-liter mixture with a red to blue liquid ratio of 17:3, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The ratio of red liquid to blue liquid is given as 17:3. This means for every 17 parts of red liquid, there are 3 parts of blue liquid.

2. **Define Variables**: Let \( x \) be a common multiplier for the parts of the liquids. Therefore, the amount of red liquid can be expressed as \( 17x \) liters and the amount of blue liquid as \( 3x \) liters.

3. **Set Up the Equation**: The total volume of the mixture is the sum of the red and blue liquids:
\[ 17x + 3x = 420 \]

4. **Combine Like Terms**: Simplifying the left side gives:
\[ 20x = 420 \]

5. **Solve for \( x \)**: To find \( x \), divide both sides of the equation by 20:
\[ x = \frac{420}{20} = 21 \]

6. **Calculate the Volume of Blue Liquid**: Now that we have \( x \), we can find the volume of blue liquid:
\[ \text{Volume of blue liquid} = 3x = 3 \times 21 = 63 \text{ liters} \]

### Conclusion:
Thus, the amount of blue liquid needed to make a 420-liter mixture is **63 liters**.

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