Question

1. find the error 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 students mistake and correct it.

Explanation:

Step1: Define the ratio

Let white paint = $w$, red paint = $r$. The ratio $w:r = 3:4$, so $\frac{w}{r} = \frac{3}{4}$.

Step2: Calculate correct white paint

Given $r = 8$, solve for $w$: $w = \frac{3}{4} \times 8 = 6$.

Step3: Identify the error

The student used absolute difference (4-3=1) instead of maintaining the ratio. Ratios require proportional scaling, not fixed differences.

Answer:

The student confused ratio with absolute difference; the correct white paint needed is 6 quarts.