To find the number of cups of fruit punch mix per 1 cup of water in Elyse’s recipe, we need to convert the mixed quantities into improper fractions and then find the unit rate.
Step 1: Convert to Improper Fractions
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Water:
- \(1 \frac{5}{4} = 1 + \frac{5}{4} = \frac{4}{4} + \frac{5}{4} = \frac{9}{4}\) cups of water.
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Fruit Punch Mix:
- \(4 \frac{3}{4} = 4 + \frac{3}{4} = \frac{16}{4} + \frac{3}{4} = \frac{19}{4}\) cups of fruit punch mix.
Step 2: Calculate the Unit Rate
To find out how many cups of fruit punch mix there are per 1 cup of water, we divide the amount of fruit punch mix by the amount of water:
\[ \text{Unit Rate} = \frac{\text{Fruit Punch Mix (cups)}}{\text{Water (cups)}} = \frac{\frac{19}{4}}{\frac{9}{4}} = \frac{19}{4} \times \frac{4}{9} = \frac{19}{9} \]
This means Elyse's recipe has \(\frac{19}{9}\) cups of fruit punch mix for every 1 cup of water.
Step 3: Repeat for Jamir's Recipe
Now let's calculate Jamir's recipe in the same way.
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Water:
- \(1 \frac{3}{1} = 1 + 3 = 4\) cups of water.
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Fruit Punch Mix:
- \(9 \frac{8}{1} = 9 + 8 = 17\) cups of fruit punch mix.
Now calculating the unit rate:
\[ \text{Unit Rate} = \frac{17}{4} \div 4 = \frac{17}{4} \times \frac{1}{4} = \frac{17}{16} \]
Comparing the Unit Rates
- Elyse's fruit punch mix per 1 cup of water: \(\frac{19}{9}\)
- Jamir's fruit punch mix per 1 cup of water: \(\frac{17}{16}\)
To compare these, we can convert them to decimals:
- \( \frac{19}{9} \approx 2.11\)
- \( \frac{17}{16} = 1.0625\)
Conclusion
Elyse’s fruit punch is fruitier than Jamir’s, as she has a higher unit rate of fruit punch mix to water in her recipe.