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Question 2:

Use what you have learned about converting between metric and imperial measurements to answer the questions.

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

• 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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1 answer

To find out if Roger can fit all the ingredients for the punch in his 8-liter bowl, we first need to convert all the ingredients from imperial units to liters.

  1. Convert each ingredient to Liters:

    • Orange Juice:

      • 2 quarts to liters:
      • \( 2 \text{ quarts} \times \frac{1 \text{ liter}}{1.06 \text{ quarts}} \approx 1.89 \text{ liters} \)

    • Cranberry Juice:

      • 3 cups to liters:
      • \( 3 \text{ cups} \times \frac{1 \text{ liter}}{4.23 \text{ cups}} \approx 0.71 \text{ liters} \)

    • Ginger Ale:

      • 1 gallon to liters:
      • \( 1 \text{ gallon} \times \frac{1 \text{ liter}}{0.26 \text{ gallons}} \approx 3.85 \text{ liters} \)

    • Pineapple Juice:

      • 1 pint to liters:
      • \( 1 \text{ pint} \times \frac{1 \text{ liter}}{2.11 \text{ pints}} \approx 0.47 \text{ liters} \)

  2. Total each ingredient:

Now, we sum all the converted quantities to see if the total fits within the 8 liters:

\[ \text{Total in liters} = 1.89 \text{ liters (orange juice)} + 0.71 \text{ liters (cranberry juice)} + 3.85 \text{ liters (ginger ale)} + 0.47 \text{ liters (pineapple juice)} \]

Adding those values:

\[ \text{Total in liters} = 1.89 + 0.71 + 3.85 + 0.47 \approx 7.92 \text{ liters} \]

  1. Compare total with bowl capacity:

The total quantity of ingredients is approximately 7.92 liters.

Since the bowl capacity is 8 liters, we can see that:

\[ 7.92 \text{ liters} < 8 \text{ liters} \]

Thus, all the ingredients will fit in the bowl.

Conclusion:

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