Bot GPT 4-o mini To find the unit rate for Elyse’s recipe, we need to determine how many cups of fruit punch mix correspond to 1 cup of water. Elyse uses \( \frac{1}{2} \frac{1}{1} \) cups of water and \( \frac{8}{1} \) cups of fruit punch mix.
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Convert the mixed numbers to improper fractions:
- For water: \( \frac{1}{2} \frac{1}{1} = \frac{3}{2} \) (since \( 1 = \frac{2}{2} \) and \( \frac{1}{2} + \frac{2}{2} = \frac{3}{2} \))
- For fruit punch mix: \( \frac{8}{1} = 8 \)
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Set up the division: We need to divide the amount of fruit punch mix by the amount of water: \[ \text{Fruit punch mix per 1 cup of water} = \frac{8}{\frac{3}{2}} = 8 \times \frac{2}{3} = \frac{16}{3} \]
Thus, Elyse’s mix has \( \frac{16}{3} \) cups of fruit punch mix per 1 cup of water.
Next, we will find the unit rate for Jamir’s recipe.
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Convert the mixed numbers to improper fractions:
- For water: \( \frac{1}{5} \frac{3}{1} = \frac{8}{5} \) (where \( 3 = \frac{15}{5} \) and \( \frac{1}{5} + \frac{15}{5} = \frac{16}{5} \))
- For fruit punch mix: \( \frac{3}{1} = 3 \)
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Set up the division: We need to divide the amount of fruit punch mix by the amount of water: \[ \text{Fruit punch mix per 1 cup of water} = \frac{3}{\frac{8}{5}} = 3 \times \frac{5}{8} = \frac{15}{8} \]
Now we can compare the results:
- Elyse's fruit punch has \( \frac{16}{3} \) cups of fruit punch mix per cup of water.
- Jamir's fruit punch has \( \frac{15}{8} \) cups of fruit punch mix per cup of water.
Now we need to convert these fractions into decimals to compare them:
- \( \frac{16}{3} \approx 5.33 \)
- \( \frac{15}{8} = 1.875 \)
Thus, Elyse's fruit punch is significantly fruitier than Jamir's fruit punch.
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