Question

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
the amount of dye (in grams) is \\(\square\\) times the amount of water (in liters).
○ not proportional

Explanation:

Step1: Check first mixture ratio

Calculate dye to water ratio for first mixture: $\frac{231}{55}$
$231\div55 = 4.2$

Step2: Check second mixture ratio

Calculate dye to water ratio for second mixture: $\frac{315}{75}$
$315\div75 = 4.2$

Step3: Check third mixture ratio

Calculate dye to water ratio for third mixture: $\frac{357}{85}$
$357\div85 = 4.2$

Since all ratios are equal (4.2), the amounts are proportional.

Answer:

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