The ratios of punch mix to water for several fruit drinks are given.

Question

Punch Mix

Mix
Water
Grape
1 cup
3 cups
Cherry
5 cups
12 cups
Lemon
7 cups
12 cups
Orange
2 cups
3 cups

Which flavor has the smallest ratio of mix to water?
grape
cherry
lemon
orange

Answer 1

To determine which flavor has the smallest ratio of punch mix to water, we need to calculate the ratio of each flavor:

1. Grape:

   • Mix: 1 cup
   • Water: 3 cups
   • Ratio: \( \frac{1}{3} \)

2. Cherry:

   • Mix: 5 cups
   • Water: 12 cups
   • Ratio: \( \frac{5}{12} \)

3. Lemon:

   • Mix: 7 cups
   • Water: 12 cups
   • Ratio: \( \frac{7}{12} \)

4. Orange:

   • Mix: 2 cups
   • Water: 3 cups
   • Ratio: \( \frac{2}{3} \)

Now we compare the ratios:

• Grape: \( \frac{1}{3} \) = 0.333
• Cherry: \( \frac{5}{12} \) ≈ 0.4167
• Lemon: \( \frac{7}{12} \) ≈ 0.5833
• Orange: \( \frac{2}{3} \) ≈ 0.6667

The smallest ratio of punch mix to water is for the grape flavor, with a ratio of \( \frac{1}{3} \).