To solve this question, let's analyze the ratios of the weight of clothing to the cups of dye for each of the given entries. The chart lists the following values:
- For 21 pounds of clothing, 3 cups of dye are needed.
- For 42 pounds of clothing, 9 cups of dye are needed.
- For 84 pounds of clothing, 12 cups of dye are needed.
- For 105 pounds of clothing, 15 cups of dye are needed.
We will calculate the ratio of the weight of the clothing to the cups of dye for each case:
1. [tex]\( \text{Ratio} = \frac{\text{Weight}}{\text{Dye}} \)[/tex]
2. Let's calculate each individually:
- For 21 pounds and 3 cups of dye:
[tex]\[
\frac{21}{3} = 7
\][/tex]
- For 42 pounds and 9 cups of dye:
[tex]\[
\frac{42}{9} \approx 4.67
\][/tex]
- For 84 pounds and 12 cups of dye:
[tex]\[
\frac{84}{12} = 7
\][/tex]
- For 105 pounds and 15 cups of dye:
[tex]\[
\frac{105}{15} = 7
\][/tex]
From the calculations, we can see that the ratios for 21 pounds (7), 84 pounds (7), and 105 pounds (7) are the same. However, the ratio for 42 pounds (approximately 4.67) is different.
Therefore, the weight of clothing for which the ratio of weight to dye is different from the others is:
42 pounds
