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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 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. Show your work.

If Roger can use the bowl, he needs to determine how many liters of liquid could still fit into the bowl. If he cannot use the bowl, he needs to determine how many extra liters of liquid there are. Round your answers to the nearest tenth of a liter. Show your work.

1 answer

To determine if Roger can fit all the ingredients for the punch in the 8-liter bowl, we'll first convert all the required ingredients to liters using the given conversion factors.

  1. Convert the ingredients to liters:

    • Orange juice: 2 quarts \[ 2 , \text{quarts} \times 1.06 , \text{liters/quart} = 2.12 , \text{liters} \]

    • Cranberry juice: 3 cups \[ 3 , \text{cups} \times \frac{1 , \text{liter}}{4.23 , \text{cups}} \approx 0.708 , \text{liters} \]

    • Ginger ale: 1 gallon \[ 1 , \text{gallon} \times \frac{1 , \text{liter}}{0.26 , \text{gallons}} \approx 3.85 , \text{liters} \]

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

  2. Calculate the total volume of all the ingredients: \[ \text{Total volume} = 2.12 , \text{liters (orange juice)} + 0.708 , \text{liters (cranberry juice)} + 3.85 , \text{liters (ginger ale)} + 0.474 , \text{liters (pineapple juice)} \] \[ \text{Total volume} \approx 2.12 + 0.708 + 3.85 + 0.474 \approx 7.152 , \text{liters} \]

  3. Compare the total volume to the bowl's capacity: The bowl holds 8 liters. The total volume of the ingredients is approximately 7.152 liters, which is less than 8 liters.

  4. Determine how much space will be left in the bowl: \[ \text{Space left} = 8 , \text{liters} - 7.152 , \text{liters} \approx 0.848 , \text{liters} \] Rounding to the nearest tenth: \[ \text{Space left} \approx 0.8 , \text{liters} \]

Conclusion: Roger can use the 8-liter bowl to mix all the ingredients, and there would be approximately 0.8 liters of space left in the bowl.