Question

question 20 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. first mixture 231 grams of dye 55 liters of water second mixture 315 grams of dye 75 liters of water third mixture 357 grams of dye 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. proportional

Explanation:

Step1: Calculate the ratio of dye to water for the first mixture

The first mixture has 231 grams of dye and 55 liters of water. The ratio is $\frac{231}{55}$.
Simplify $\frac{231}{55}$: divide numerator and denominator by 11, we get $\frac{21}{5} = 4.2$.

Step2: Calculate the ratio of dye to water for the second mixture

The second mixture has 315 grams of dye and 75 liters of water. The ratio is $\frac{315}{75}$.
Simplify $\frac{315}{75}$: divide numerator and denominator by 15, we get $\frac{21}{5} = 4.2$.

Step3: Calculate the ratio of dye to water for the third mixture

The third mixture has 357 grams of dye and 85 liters of water. The ratio is $\frac{357}{85}$.
Simplify $\frac{357}{85}$: divide numerator and denominator by 17, we get $\frac{21}{5} = 4.2$.

Since the ratio of dye to water is the same (4.2) for all three mixtures, the amounts are proportional.

Answer:

Proportional (the constant of proportionality is 4.2)