Question 1 Roger is planning a party. He needs these ingredients in the following quantities to make punch: quarts orange juice cups cranberry juice ginger ale 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 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, , , and
To determine if all the ingredients can fit in the bowl, we need to convert the quantities into the same unit of measurement.
1 quart is equal to 4 cups.
3 cups is already in cups.
1 pint is equal to 2 cups.
So the total quantity in the bowl will be:
4 cups of orange juice + 3 cups of cranberry juice + 2 cups of ginger ale + 2 cups of pineapple juice = 11 cups.
Now let's convert the measurement of the bowl into cups.
quarts is equal to 8 cups.
If the bowl can hold cups of liquid, and the total quantity needed is 11 cups, then the bowl can fit all the ingredients and there would be no extra space.
Therefore, Roger can use the bowl to mix all the ingredients for the punch.
To determine if Roger can fit all the ingredients in the bowl, let's convert the quantities of each ingredient to cups:
- Quarts to cups: There are 4 cups in a quart. So, Roger needs 8 quarts of orange juice, which is equal to 32 cups (8 x 4).
- Pint to cups: There are 2 cups in a pint. Roger needs 1 pint of pineapple juice, which is equal to 2 cups.
- Cups: Cranberry juice and ginger ale are already measured in cups.
Now let's add up the quantities:
32 cups (orange juice) + 2 cups (cranberry juice) + 2 cups (ginger ale) + 2 cups (pineapple juice) = 38 cups of liquid.
Since we need to convert the capacity of the bowl to cups, let's use the following measurement equivalents:
- 1 liter is approximately 4.227 cups. So, the bowl's capacity is 60 cups ( = 14.22 x 60).
Comparing the amount of liquid needed (38 cups) to the bowl's capacity (60 cups), we see that Roger can indeed fit all the ingredients in the bowl.
To determine how much more liquid can fit in the bowl (if any), we subtract the amount of liquid needed (38 cups) from the bowl's capacity (60 cups):
60 cups (bowl's capacity) - 38 cups (liquid needed) = 22 cups.
So, there is space in the bowl for an additional 22 cups of liquid.
Converted to liters, with 1 liter being approximately 4.227 cups:
22 cups / 4.227 = 5.2 liters.
Therefore, if the bowl is used, there would be space for approximately 5.2 liters of additional liquid.
To determine if all the ingredients can fit in the bowl, we need to convert the quantities of each ingredient into the same unit of measure.
Given measurement equivalents:
1 quart = 4 cups
1 pint = 2 cups
Quantities of ingredients required for the punch:
- Orange juice: quarts
- Cranberry juice: cups
- Ginger ale: cups
- Pineapple juice: pint
Converting the quantities:
- Orange juice: quarts = quarts * 4 cups/quart = cups
- Cranberry juice: cups
- Ginger ale: cups
- Pineapple juice: pint = pint * 2 cups/pint = cups
Now, let's add up the quantities:
- Total quantity = cups + cups + cups + cups
Next, we need to check if the total quantity can fit into the bowl that holds cups of liquid.
If the total quantity is less than or equal to the capacity of the bowl ( cups), then Roger can use the bowl to mix all the ingredients.
If the total quantity is greater than the capacity of the bowl, then Roger cannot use the bowl to mix all the ingredients.
To determine how many extra liters of liquid there are if the total quantity exceeds the bowl's capacity:
- Calculate the excess quantity = total quantity - bowl capacity
To convert the excess quantity from cups to liters:
- 1 cup ≈ 0.2366 liters
- excess quantity (in liters) = excess quantity (in cups) * 0.2366
By following these steps, you can determine if Roger can use the bowl to mix all the ingredients and find out how much extra liquid there may be.