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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.

1 answer

To determine if Roger's 8-liter bowl can hold all the ingredients for the punch, we need to convert the quantities of each ingredient into liters and then sum them up.

Ingredients in Imperial Measurements:

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

Conversion Values:

  • 1 liter ≈ 4.23 cups
  • 1 liter ≈ 2.11 pints
  • 1 liter ≈ 1.06 quarts
  • 1 liter ≈ 0.26 gallons

Conversion Calculations:

  1. Orange Juice: 2 quarts

    • \( 2 , \text{quarts} \times \frac{1 , \text{liter}}{1.06 , \text{quarts}} \approx 1.887 , \text{liters} \)

  2. Cranberry Juice: 3 cups

    • \( 3 , \text{cups} \times \frac{1 , \text{liter}}{4.23 , \text{cups}} \approx 0.710 , \text{liters} \)

  3. Ginger Ale: 1 gallon

    • \( 1 , \text{gallon} \times \frac{1 , \text{liter}}{0.26 , \text{gallons}} \approx 3.846 , \text{liters} \)

  4. Pineapple Juice: 1 pint

    • \( 1 , \text{pint} \times \frac{1 , \text{liter}}{2.11 , \text{pints}} \approx 0.474 , \text{liters} \)

Total Volume Calculation in Liters:

Now, let's sum up all the volumes in liters:

\[ \text{Total Volume} = 1.887 , \text{liters} + 0.710 , \text{liters} + 3.846 , \text{liters} + 0.474 , \text{liters} \]

Calculating the total:

\[ \text{Total Volume} \approx 1.887 + 0.710 + 3.846 + 0.474 \approx 7.917 , \text{liters} \]

Comparison with Bowl Capacity:

Roger's bowl can hold 8 liters. Since 7.917 liters is less than 8 liters, all the ingredients will fit in the bowl.

Final Answer:

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