Question

here are the instructions for cooking instant rice in the microwave.
ingredients
cook time

1. which relationships are proportional (if any)?
2. for any proportional relationships, determine a constant of proportionality and explain what it means.

Explanation:

Step1: Check proportion for Ingredients table

For Ingredients:

• When rice \(r = 1\), water \(w=1\frac{1}{2}=\frac{3}{2}\), \(\frac{w}{r}=\frac{3}{2}\)
• When \(r = 2\), \(w = 3\), \(\frac{w}{r}=\frac{3}{2}\)
• When \(r=3\), \(w = 4\frac{1}{2}=\frac{9}{2}\), \(\frac{w}{r}=\frac{3}{2}\)

Step2: Check proportion for Cook Time table

For Cook Time:

• When rice \(r = 1\), time \(t = 7\), \(\frac{t}{r}=7\)
• When \(r = 2\), \(t = 11\), \(\frac{t}{r}=\frac{11}{2}=5.5\)
• Since \(7

eq5.5\), Cook - Time is not proportional

Answer:

1. The relationship between rice and water (Ingredients table) is proportional. The relationship between rice and cook - time (Cook Time table) is not proportional.
2. The constant of proportionality \(k=\frac{3}{2}\). It means that for every cup of rice, \(\frac{3}{2}\) cups of water are needed.