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

Question

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

Answer 1

To determine if Roger can fit all the ingredients for the punch into his 8-liter bowl, we'll first convert the quantities of each ingredient to liters and then add them up.

1. Convert each ingredient to liters:

• Orange Juice:

  • 2 quarts to liters: \[ 2 , \text{quarts} \times \frac{1 , \text{liter}}{1.06 , \text{quarts}} \approx 1.887 , \text{liters} \]

• Cranberry Juice:

  • 3 cups to liters: \[ 3 , \text{cups} \times \frac{1 , \text{liter}}{4.23 , \text{cups}} \approx 0.709 , \text{liters} \]

• Ginger Ale:

  • 1 gallon to liters: \[ 1 , \text{gallon} \times \frac{1 , \text{liter}}{0.26 , \text{gallons}} \approx 3.846 , \text{liters} \]

• Pineapple Juice:

  • 1 pint to liters: \[ 1 , \text{pint} \times \frac{1 , \text{liter}}{2.11 , \text{pints}} \approx 0.474 , \text{liters} \]

2. Add the volumes in liters: \[ 1.887 , \text{liters (orange juice)} + 0.709 , \text{liters (cranberry juice)} + 3.846 , \text{liters (ginger ale)} + 0.474 , \text{liters (pineapple juice)} \approx 7.916 , \text{liters} \]

3. Compare the total volume with the bowl capacity:

• The bowl holds 8 liters.
• The total volume needed for the punch is approximately 7.916 liters.

Since \(7.916 , \text{liters} < 8 , \text{liters}\), all the ingredients will fit in the 8-liter bowl.

Final Response: Yes, Roger can use the 8-liter bowl to mix all the ingredients for the punch.