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. Show your work.
If he 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.
1 liter is about 4.23 cups, 2.11 pints, 1.06 quarts, and 0.26 gallons
To determine if Roger can fit all of the ingredients in the 8-liter bowl, we need to convert the quantities of each ingredient into liters and then add them together.
First, let's convert each ingredient:
- 2 quarts of orange juice:
2 quarts = 2.11 liters
- 3 cups of cranberry juice:
3 cups = 0.71 liters
- 1 gallon of ginger ale:
1 gallon = 3.79 liters
- 1 pint of pineapple juice:
1 pint = 0.47 liters
Now, let's add all the quantities together:
2.11 liters + 0.71 liters + 3.79 liters + 0.47 liters = 7.08 liters
Since the total quantity of the ingredients is less than 8 liters, Roger can use the 8-liter bowl to mix all the ingredients for the punch.
To determine how many liters of liquid could still fit into the bowl, we subtract the total quantity of the ingredients from the bowl's capacity:
8 liters - 7.08 liters = 0.92 liters
Therefore, 0.92 liters of liquid could still fit into the bowl.
To determine if Roger can use the 8-liter bowl to mix all the ingredients for the punch, we need to convert the quantities of each ingredient to liters.
1. Convert 2 quarts of orange juice to liters:
2 quarts = 2.11 liters
2. Convert 3 cups of cranberry juice to liters:
3 cups = 0.71 liters
3. Convert 1 gallon of ginger ale to liters:
1 gallon = 3.79 liters
4. Convert 1 pint of pineapple juice to liters:
1 pint = 0.47 liters
Now, let's calculate the total amount of liquid needed for the punch:
Total = 2.11 + 0.71 + 3.79 + 0.47 = 7.08 liters
Since the total amount of liquid needed for the punch is less than the capacity of the 8-liter bowl, Roger can use the bowl.
To determine how many liters of liquid could still fit into the bowl, we subtract the total amount of liquid needed for the punch from the bowl capacity:
Leftover = 8 - 7.08 = 0.92 liters
Therefore, if Roger uses the 8-liter bowl, there would be approximately 0.9 liters of free space remaining.
To determine if Roger can use the 8-liter bowl to mix all the ingredients for the punch, we need to convert the given quantities of each ingredient into liters and add them up. Here's how you can do it:
1. Start with the given quantities of each ingredient:
- 2 quarts orange juice
- 3 cups cranberry juice
- 1 gallon ginger ale
- 1 pint pineapple juice
2. Convert the quantities into liters using the provided measurement equivalents:
- 2 quarts = 2 x 1.06 = 2.12 liters
- 3 cups = 3 x 4.23 / 33.81 = 0.38 liters
- 1 gallon = 1 x 3.79 = 3.79 liters
- 1 pint = 1 x 2.11 / 33.81 = 0.06 liters
3. Add up the converted quantities:
2.12 + 0.38 + 3.79 + 0.06 = 6.35 liters
Now we have the total amount of liquid needed to make the punch, which is 6.35 liters.
4. Compare the total amount of liquid needed (6.35 liters) with the capacity of the bowl (8 liters).
- If the total amount of liquid needed is less than or equal to the capacity of the bowl (6.35 ≤ 8), then Roger can use the bowl to mix all the ingredients.
- If the total amount of liquid needed is greater than the capacity of the bowl (6.35 > 8), then Roger cannot use the bowl to mix all the ingredients.
In this case, 6.35 is indeed less than 8, so Roger can use the 8-liter bowl to mix all the ingredients.
To determine how many liters of liquid could still fit into the bowl, subtract the total amount of liquid needed from the bowl's capacity:
8 - 6.35 = 1.65 liters
Therefore, if Roger uses the 8-liter bowl to mix the punch, there would be approximately 1.7 liters of space remaining in the bowl.