Roger is planning a party. He needs these ingredients in the following quantities to make punch:

Question

• 2 quarts orange juice

• 3 cups cranberry juice

• 1 gallon ginger ale

• 1 pint pineapple juice



Roger knows he will need a relatively large container to mix the punch. Unfortunately, all he can find is a bowl that holds 8 liters of liquid. He is not sure whether he can fit all of the ingredients in the bowl at the same time. Use the following measurement equivalents to determine if Roger can use the 8 liter bowl to mix all the ingredients for the punch.

1 liter is about 4.23 cups, 2.11 pints, 1.06 quarts, and 0.26 gallons

Will all the ingredients for the party punch fit in Roger's 8 liter bowl?

Be sure to work out the problem on paper and use a calculator if needed.

(2 points)
Responses

No, the bowl is too small and the ingredients will not all fit.
No, the bowl is too small and the ingredients will not all fit.

Yes, the bowl is big enough for all the ingredients for Roger's party punch.
Yes, the bowl is big enough for all the ingredients for Roger's party punch.
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Answer 1

To determine if Roger can fit all the ingredients into the 8-liter bowl, we first need to convert all the ingredients into the same unit (liters) and then see if their total volume is greater than 8 liters.

Ingredients and Their Quantities

1. Orange Juice: 2 quarts
2. Cranberry Juice: 3 cups
3. Ginger Ale: 1 gallon
4. Pineapple Juice: 1 pint

Conversion Breakdown

1. Orange Juice:

   \[ 2 \text{ quarts} \times 1.06 \text{ liters/quart} = 2.12 \text{ liters} \]

2. Cranberry Juice:

   \[ 3 \text{ cups} \div 4.23 \text{ cups/liter} \approx 0.709 \text{ liters} \]

3. Ginger Ale:

   \[ 1 \text{ gallon} \div 0.26 \text{ gallons/liter} \approx 3.85 \text{ liters} \]

4. Pineapple Juice:

   \[ 1 \text{ pint} \div 2.11 \text{ pints/liter} \approx 0.474 \text{ liters} \]

Total Volume Calculation

Now we will sum the volumes we calculated above:

\[ \text{Total Volume} = 2.12 + 0.709 + 3.85 + 0.474 \]

Calculating the sum:

\[ 2.12 + 0.709 = 2.829 \] \[ 2.829 + 3.85 \approx 6.679 \] \[ 6.679 + 0.474 \approx 7.153 \]

Conclusion

The total volume of the ingredients is approximately 7.153 liters. Since 7.153 liters is less than 8 liters, Roger can fit all the ingredients into the bowl.

Answer: Yes, the bowl is big enough for all the ingredients for Roger's party punch.