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Answer :
To solve this question, we need to identify which weight of clothing has a different ratio of weight to dye compared to the others. The table provides us with the weight of clothing in pounds and the corresponding amount of dye.
Let's find the ratio of weight to dye for each clothing weight:
1. For 21 pounds of clothing with 3 units of dye, the ratio is:
[tex]\[
\frac{21}{3} = 7
\][/tex]
2. For 42 pounds of clothing with 9 units of dye, the ratio is:
[tex]\[
\frac{42}{9} \approx 4.67
\][/tex]
3. For 84 pounds of clothing with 12 units of dye, the ratio is:
[tex]\[
\frac{84}{12} = 7
\][/tex]
4. For 105 pounds of clothing with 15 units of dye, the ratio is:
[tex]\[
\frac{105}{15} = 7
\][/tex]
These calculated ratios show that:
- The ratios for 21 pounds, 84 pounds, and 105 pounds are all 7.
- The ratio for 42 pounds is approximately 4.67, which is different from the others.
Therefore, the weight of clothing with a different ratio is 42 pounds.
Let's find the ratio of weight to dye for each clothing weight:
1. For 21 pounds of clothing with 3 units of dye, the ratio is:
[tex]\[
\frac{21}{3} = 7
\][/tex]
2. For 42 pounds of clothing with 9 units of dye, the ratio is:
[tex]\[
\frac{42}{9} \approx 4.67
\][/tex]
3. For 84 pounds of clothing with 12 units of dye, the ratio is:
[tex]\[
\frac{84}{12} = 7
\][/tex]
4. For 105 pounds of clothing with 15 units of dye, the ratio is:
[tex]\[
\frac{105}{15} = 7
\][/tex]
These calculated ratios show that:
- The ratios for 21 pounds, 84 pounds, and 105 pounds are all 7.
- The ratio for 42 pounds is approximately 4.67, which is different from the others.
Therefore, the weight of clothing with a different ratio is 42 pounds.
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