To determine whether Roger can fit all the ingredients for the punch in an 8-liter bowl, let's first convert all the quantities of the ingredients to liters. We'll use the provided conversion factors for this calculation.
Ingredients and Their Quantities:
-
Orange Juice: 2 quarts
- Conversion: \(2 \text{ quarts} \times 0.946 \text{ liters/quart} = 1.892 \text{ liters}\)
-
Cranberry Juice: 3 cups
- Conversion: \(3 \text{ cups} \div 4.23 \text{ cups/liter} \approx 0.708 \text{ liters}\)
-
Ginger Ale: 1 gallon
- Conversion: \(1 \text{ gallon} \times 3.785 \text{ liters/gallon} = 3.785 \text{ liters}\)
-
Pineapple Juice: 1 pint
- Conversion: \(1 \text{ pint} \div 2.11 \text{ pints/liter} \approx 0.474 \text{ liters}\)
Total Volume Calculation in Liters:
Now we will sum the volumes of all the ingredients:
\[ \text{Total Volume} = \text{Orange Juice} + \text{Cranberry Juice} + \text{Ginger Ale} + \text{Pineapple Juice} \]
\[ \text{Total Volume} = 1.892 + 0.708 + 3.785 + 0.474 \]
\[ \text{Total Volume} \approx 7.859 \text{ liters} \]
Determining Capacity:
Now, we compare this total volume with the capacity of the bowl.
- Capacity of the bowl: 8 liters
- Total volume of the ingredients: 7.859 liters
Since \(7.859 \text{ liters} < 8 \text{ liters}\), Roger can use the bowl to fit all the ingredients.
How Many Extra Liters Could Still Fit Into the Bowl:
To find out how many liters could still fit into the bowl:
\[ \text{Extra Capacity} = \text{Capacity of the bowl} - \text{Total Volume} \]
\[ \text{Extra Capacity} = 8 \text{ liters} - 7.859 \text{ liters} \approx 0.141 \text{ liters} \]
Final Answer:
- Roger can use the 8-liter bowl.
- Extra capacity in the bowl after adding all the ingredients is approximately 0.1 liters (rounded to the nearest tenth).
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