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The problem asks to find the student's mistake and correct it. The student believes that if the ratio of white paint to red paint is \(3:4\), and if they have 8 quarts of red paint, they will need 7 quarts of white paint to maintain the same ratio. This assumption is incorrect. Let's break it down:

### Given Information:
- The original ratio of white paint to red paint is \(3:4\).
- The student has 8 quarts of red paint.
- The student incorrectly thinks that 7 quarts of white paint will maintain the same ratio.

### Analyzing the Ratio:
The correct interpretation of the ratio \(3:4\) is that for every 3 parts of white paint, there should be 4 parts of red paint. If the amount of red paint is 8 quarts, we need to find the corresponding amount of white paint using the ratio.

The ratio can be written as:
\[
\frac{\text{White Paint}}{\text{Red Paint}} = \frac{3}{4}
\]
Substitute the given value for red paint (8 quarts):
\[
\frac{\text{White Paint}}{8} = \frac{3}{4}
\]
Now, solve for the amount of white paint:
\[
\text{White Paint} = \frac{3}{4} \times 8 = 6 \text{ quarts}
\]

### Conclusion:
The student made a mistake by thinking that 7 quarts of white paint is needed, but the correct amount of white paint required to maintain the \(3:4\) ratio with 8 quarts of red paint is 6 quarts.

Would you like more details or have any further questions?

Here are five related questions for further practice:
1. If the ratio of white paint to red paint is \(5:6\), how much white paint is needed if you have 12 quarts of red paint?
2. If you have 15 quarts of white paint and the ratio of white paint to red paint is \(3:5\), how much red paint is required?
3. How would the ratio change if the amount of white paint was doubled while the red paint stayed the same?
4. Can you express the ratio \(3:4\) as a decimal and percentage?
5. If the total amount of paint (white and red combined) is 20 quarts, and the ratio of white to red paint is \(3:4\), how many quarts of each do you have?

**Tip:** When dealing with ratios, always set up a proportion to ensure that the correct relationship between the quantities is maintained.

The ratio of quarts of white paint to red paint is 3:4. A student says that to maintain the same ratio, he will need 7 quarts of white paint if he has 8 quarts of red paint, because originally there was one more quart of red paint than white paint. Find the student's mistake and correct it.

This problem involves correcting a student's misunderstanding of how to maintain a 3:4 ratio between white paint and red paint. The correct solution demonstrates how to use proportions to find the appropriate amount of white paint when the quantity of red paint is given. Suitable for Grades 6-8.

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