Question

a manufacturer made three mixtures of powdered dye and water. the first mixture has 231 grams of powdered dye and 55 liters of water. the second mixture has 315 grams of powdered dye and 75 liters of water. the third mixture has 357 grams of powdered dye and 85 liters of water. state whether the amount of dye and amount of water are proportional for the three mixtures. if they are proportional, fill in the blank with a whole number or a decimal. the amount of dye (in grams) is times the amount of water (in liters). options: proportional, not proportional

Explanation:

Step1: Calculate dye-to-water ratio (1st)

$\frac{231}{55} = 4.2$

Step2: Calculate dye-to-water ratio (2nd)

$\frac{315}{75} = 4.2$

Step3: Calculate dye-to-water ratio (3rd)

$\frac{357}{85} = 4.2$

Step4: Compare ratios and confirm

All ratios equal 4.2, so proportional.

Answer:

Proportional
The amount of dye (in grams) is $4.2$ times the amount of water (in liters).