To determine whether Roger can fit all the ingredients for the punch into an 8-liter bowl, we need to convert the quantities of each ingredient to liters using the provided measurement equivalents.
Step 1: Convert each ingredient to liters.
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Orange Juice: \[ 2 \text{ quarts} \times \frac{1.06 \text{ liters}}{1 \text{ quart}} = 2.12 \text{ liters} \]
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Cranberry Juice: \[ 3 \text{ cups} \times \frac{1 \text{ liter}}{4.23 \text{ cups}} \approx 0.709 \text{ liters} \]
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Ginger Ale: \[ 1 \text{ gallon} \times \frac{1 \text{ liter}}{0.26 \text{ gallons}} \approx 3.85 \text{ liters} \]
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Pineapple Juice: \[ 1 \text{ pint} \times \frac{1 \text{ liter}}{2.11 \text{ pints}} \approx 0.474 \text{ liters} \]
Step 2: Sum the converted quantities
Now we will sum all the converted quantities in liters: \[ \text{Total Volume} = \text{Orange Juice} + \text{Cranberry Juice} + \text{Ginger Ale} + \text{Pineapple Juice} \] \[ \text{Total Volume} = 2.12 + 0.709 + 3.85 + 0.474 \approx 7.153 \text{ liters} \]
Step 3: Compare total volume to bowl capacity
The bowl holds 8 liters. Since we have a total volume of approximately 7.153 liters, we can fit all the ingredients into the bowl.
Step 4: Calculate remaining space in the bowl
To find out how many liters will still fit into the bowl: \[ \text{Remaining space} = \text{Bowl capacity} - \text{Total Volume} \] \[ \text{Remaining space} = 8 \text{ liters} - 7.153 \text{ liters} \approx 0.847 \text{ liters} \]
Final Answers:
- Roger can use the 8-liter bowl with approximately 0.8 liters of space remaining (rounded to the nearest tenth of a liter).
3 answers