Question 1 Roger is planning a party. He needs these ingredients in the following quantities to make punch: 2quarts orange juice 3cups cranberry juice 1 gallon ginger ale 1pint 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 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 bowl to mix all the ingredients for the punch. Show your work. If he can use the bowl, he needs to determine how many 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. is about cups, , 1liter is about 4.23 cups 2.11 pints 1.06 quarts and 0.26 gallons
To determine whether Roger can fit all the ingredients in the bowl, we need to convert all the measurements to cups.
2 quarts = 2 * 4 = 8 cups
3 cups cranberry juice = 3 cups
1 gallon = 1 * 16 = 16 cups
1 pint = 1 * 2 = 2 cups
Total volume of ingredients = 8 cups + 3 cups + 16 cups + 2 cups = 29 cups
Let's assume the bowl can hold x cups of liquid.
If the bowl can hold at least 29 cups, then Roger can use the bowl to mix all the ingredients.
If the bowl cannot hold 29 cups, then we need to determine how many extra liters of liquid there are.
1 liter = 4.23 cups
So, if the bowl cannot hold 29 cups, then the extra liters of liquid would be:
(x cups - 29 cups) / 4.23 cups = extra liters of liquid
Round the answer to the nearest tenth of a liter.
To determine if Roger can use the bowl to mix all the ingredients, we need to calculate the total volume of the ingredients and compare it to the capacity of the bowl.
First, let's convert the quantities of each ingredient to liters using the measurement equivalents provided:
- 2 quarts of orange juice = 2.11 * 2 = 4.22 liters
- 3 cups of cranberry juice = 3 / 4.23 = 0.71 liters
- 1 gallon of ginger ale = 3.78 liters
- 1 pint of pineapple juice = 2.11 * 1 = 2.11 liters
Now, let's calculate the total volume of the ingredients:
4.22 + 0.71 + 3.78 + 2.11 = 10.82 liters
Next, we compare this to the capacity of the bowl. Let's assume the bowl can hold x liters of liquid.
If the total volume of the ingredients is less than or equal to the capacity of the bowl (10.82 <= x), then Roger can use the bowl to mix all the ingredients.
If the total volume of the ingredients is greater than the capacity of the bowl (10.82 > x), then Roger cannot use the bowl.
To determine how many extra liters of liquid there are if Roger cannot use the bowl, we subtract the capacity of the bowl from the total volume of the ingredients:
Extra liters = 10.82 - x
Please provide the capacity of the bowl in liters, and I can calculate whether Roger can use the bowl and how many extra liters there would be if he cannot.
To determine if Roger can use the bowl to mix all the ingredients for the punch, we need to calculate the total volume of the ingredients and compare it to the capacity of the bowl.
First, let's convert all the given measurements to quarts for consistency:
2 quarts of orange juice
3 cups of cranberry juice = 3/4 quarts (since 1 cup is 1/4 of a quart)
1 gallon of ginger ale = 4 quarts
1 pint of pineapple juice = 1/2 quart (since 1 pint is 1/2 of a quart)
Now, let's calculate the total volume of the ingredients:
Total volume = 2 quarts (orange juice) + 3/4 quarts (cranberry juice) + 4 quarts (ginger ale) + 1/2 quart (pineapple juice)
Total volume = 2 + 3/4 + 4 + 1/2 quarts
To add the fractions, we must have a common denominator. In this case, the common denominator is 4:
Total volume = 2 + 3/4 + 4 + 2/4 quarts
Total volume = 2 + 5/4 + 4 quarts
Total volume = 9 + 5/4 quarts
Total volume = 9.25 quarts
Now, let's check if the bowl can accommodate this volume:
If 1 liter is about 4.23 cups, then 1 quart is about 4.23 cups.
Let's convert the volume of the bowl to quarts:
The bowl holds 3 quarts.
Since the total volume of the ingredients is 9.25 quarts, we can conclude that Roger cannot use the bowl to mix all the ingredients for the punch.
To determine how many extra liters of liquid there are, we need to find the difference between the total volume of the ingredients (in liters) and the capacity of the bowl (in liters):
Total volume of the ingredients in liters = 9.25 quarts * (1 liter / 4.23 cups) * (1 cup / 0.26 gallons) * (1 gallon / 4 quarts)
Total volume of the ingredients in liters ≈ 2.19 liters
Capacity of the bowl in liters = 3 quarts * (1 liter / 4.23 cups) * (1 cup / 0.26 gallons) * (1 gallon / 4 quarts)
Capacity of the bowl in liters ≈ 0.71 liters
Extra liters of liquid = Total volume of the ingredients (in liters) - Capacity of the bowl (in liters)
Extra liters of liquid ≈ 2.19 liters - 0.71 liters
Extra liters of liquid ≈ 1.48 liters
Therefore, there are approximately 1.48 extra liters of liquid that cannot fit in the bowl.