To find out which flavor has the smallest ratio of punch mix to water, we need to determine the ratio of punch mix to water for each flavor. We'll express these ratios as fractions and then compare them.
Step-by-step breakdown:
1. Grape Punch:
- The given information is 1 cup of mix to 3 cups of water.
- This ratio can be written as a fraction: [tex]\( \frac{1}{3} \)[/tex].
2. Cherry Punch:
- The given information is 5 cups of mix to 12 cups of water.
- This ratio can be written as a fraction: [tex]\( \frac{5}{12} \)[/tex].
3. Lemon Punch:
- The given information is 7 cups of mix to 12 cups of water.
- This ratio can be written as a fraction: [tex]\( \frac{7}{12} \)[/tex].
4. Orange Punch:
- The given information is 2 cups of mix to 3 cups of water.
- This ratio can be written as a fraction: [tex]\( \frac{2}{3} \)[/tex].
Now, we will convert these fractions to their decimal forms to easily compare them:
- Grape: [tex]\( \frac{1}{3} \)[/tex] = 0.333...
- Cherry: [tex]\( \frac{5}{12} \)[/tex] = 0.416...
- Lemon: [tex]\( \frac{7}{12} \)[/tex] = 0.583...
- Orange: [tex]\( \frac{2}{3} \)[/tex] = 0.666...
Comparing these values:
- Grape: 0.333...
- Cherry: 0.416...
- Lemon: 0.583...
- Orange: 0.666...
The smallest decimal value among these is 0.333..., which corresponds to the Grape punch mix.
Therefore, the flavor with the smallest ratio of punch mix to water is:
grape.
