The ratio of dye to pounds of clothing is constant. A worker develops the chart below to show the amount of dye needed for different amounts of clothing.

Question

Clothes Dyeing
Weight of clothing (pounds)
Cups of dye
21
3
42
9
84
12
105
15

For which weight of clothing is the ratio of weight to dye different from the other ratios?
21 pounds
42 pounds
84 pounds
105 pounds

Answer 1

To determine which weight of clothing has a different ratio of weight to dye, we can calculate the ratio of pounds of clothing to cups of dye for each given weight.

1. For 21 pounds: \[ \text{Ratio} = \frac{21 \text{ pounds}}{3 \text{ cups}} = 7 \text{ pounds per cup} \]

2. For 42 pounds: \[ \text{Ratio} = \frac{42 \text{ pounds}}{9 \text{ cups}} = \frac{42}{9} \approx 4.67 \text{ pounds per cup} \]

3. For 84 pounds: \[ \text{Ratio} = \frac{84 \text{ pounds}}{12 \text{ cups}} = 7 \text{ pounds per cup} \]

4. For 105 pounds: \[ \text{Ratio} = \frac{105 \text{ pounds}}{15 \text{ cups}} = 7 \text{ pounds per cup} \]

Now, let's summarize the ratios:

• 21 pounds: 7 pounds per cup
• 42 pounds: approximately 4.67 pounds per cup
• 84 pounds: 7 pounds per cup
• 105 pounds: 7 pounds per cup

From these calculations, we can see that the ratio for 42 pounds (approximately 4.67 pounds per cup) is different from the others. Therefore, the weight of clothing for which the ratio is different is 42 pounds.