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 of 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 whether 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.
Roger also wants to make sandwiches for his guests. He buys the following sandwich fillings: 1.5 kilograms of turkey 1.25 kilograms of beef 2.25 pounds of cheese
Roger wants to know whether he purchased more turkey or more cheese. Use the conversion ratio 1 kilogram = about 2.2 pounds to determine the correct answer. Show your work.
Roger discovers that he needs to buy some chicken as well. He buys an amount of chicken that weighs more than the beef he bought and less than the turkey he bought. Give an amount in pounds that the chicken could weigh, rounded to the nearest hundredth of a pound. Show your work.
Roger is curious to know the total weight of all four sandwich fillings he bought. He weighs the fillings twice, once using ounces and once using grams. If 16 ounces = 1 pound and 1,000 grams = 1 kilogram, will the total weight of the sandwich fillings be a greater number of ounces or a greater number of grams? Explain your answer.
To determine whether Roger can use the 8-liter bowl to mix all the ingredients for the punch, we need to convert the quantities of the ingredients to liters:
2 quarts = 2.11 liters
3 cups = 0.71 liters
1 gallon = 3.78 liters
1 pint = 0.47 liters
Now let's add up the quantities of the ingredients:
2.11 liters + 0.71 liters + 3.78 liters + 0.47 liters = 7.07 liters
Since the total quantity of the ingredients is less than the capacity of the bowl (8 liters), Roger can use the 8-liter bowl to mix all the ingredients for the punch. The amount of space left in the bowl would be 8 liters - 7.07 liters = 0.93 liters.
To determine whether Roger purchased more turkey or more cheese, we need to convert the quantities to pounds:
1.5 kg = 3.3 pounds (rounded to the nearest tenth)
2.25 pounds = 2.25 pounds
Since 3.3 pounds is greater than 2.25 pounds, Roger purchased more turkey than cheese.
To find the amount of chicken that weighs more than the beef but less than the turkey, we can use the given conversion ratio:
1.25 kg = 2.75 pounds (rounded to the nearest tenth)
The chicken could weigh 2.75 pounds.
To compare the total weight of the sandwich fillings in ounces and grams, we need to convert the quantities to the same unit. Since the given conversion ratios are 16 ounces = 1 pound and 1,000 grams = 1 kilogram, we can convert all the quantities to grams:
1.5 kg = 1,500 grams
1.25 kg = 1,250 grams
2.25 pounds = 1,017 grams (rounded to the nearest whole number)
In grams, the total weight of the sandwich fillings is 1,500 + 1,250 + 1,017 = 3,767 grams.
Now let's convert the quantities to ounces:
1.5 kg = 52.92 ounces (rounded to the nearest hundredth)
1.25 kg = 44.09 ounces (rounded to the nearest hundredth)
2.25 pounds = 36.00 ounces
In ounces, the total weight of the sandwich fillings is 52.92 + 44.09 + 36.00 = 132.01 ounces.
Therefore, the total weight of the sandwich fillings is a greater number of grams (3,767 grams) than ounces (132.01 ounces).