To determine if Roger can fit all the ingredients into an 8-liter bowl, we first need to convert all the ingredients into liters using the provided measurement equivalents.
Ingredient quantities:
- Orange juice: 2 quarts
- Cranberry juice: 3 cups
- Ginger ale: 1 gallon
- Pineapple juice: 1 pint
Step 1: Convert each ingredient to liters.
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Orange juice (2 quarts):
- Conversion: 1 quart ≈ 0.946 liters \[ 2 \text{ quarts} \times 0.946 \text{ liters/quart} = 1.892 \text{ liters} \]
-
Cranberry juice (3 cups):
- Conversion: 1 liter ≈ 4.23 cups \[ 3 \text{ cups} \times \frac{1 \text{ liter}}{4.23 \text{ cups}} \approx 0.709 \text{ liters} \]
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Ginger ale (1 gallon):
- Conversion: 1 gallon ≈ 3.785 liters \[ 1 \text{ gallon} \approx 3.785 \text{ liters} \]
-
Pineapple juice (1 pint):
- Conversion: 1 pint ≈ 0.473 liters \[ 1 \text{ pint} \approx 0.473 \text{ liters} \]
Step 2: Add up all the converted amounts. \[ \text{Total volume} = (1.892 \text{ liters}) + (0.709 \text{ liters}) + (3.785 \text{ liters}) + (0.473 \text{ liters}) \]
Calculating the total: \[ 1.892 + 0.709 + 3.785 + 0.473 = 7.859 \text{ liters} \]
Step 3: Compare with the bowl's capacity (8 liters).
Since \( 7.859 \text{ liters} < 8 \text{ liters} \), Roger can use the bowl.
Step 4: Calculate how much space will be left in the bowl. \[ \text{Extra space} = 8 \text{ liters} - 7.859 \text{ liters} = 0.141 \text{ liters} \]
Final Answer: Roger can use the 8-liter bowl, and there will be approximately 0.1 liters of extra space left in the bowl.
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