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.
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 if 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 if Roger can use the 8-liter bowl to mix all the ingredients for the punch, we need to convert the quantities given into liters and check if the total is less than or equal to 8 liters.
1. Convert the quantities given into liters:
- 2 quarts orange juice = 2 x 1.06 = 2.12 liters
- 3 cups cranberry juice = 3 x 0.24 = 0.72 liters
- 1 gallon ginger ale = 1 x 3.78 = 3.78 liters
- 1 pint pineapple juice = 1 x 0.47 = 0.47 liters
2. Add up the converted quantities:
2.12 + 0.72 + 3.78 + 0.47 = 7.09 liters
Since the total quantity 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 need to subtract the total quantity from the bowl capacity of 8 liters.
8 - 7.09 = 0.91 liters
Therefore, if Roger uses the 8-liter bowl, there will be about 0.91 liters of space remaining.
To determine if Roger purchased more turkey or more cheese, we need to convert the quantities given into a common unit (pounds).
1. Convert the quantities given into pounds:
- 1.5 kilograms of turkey = 1.5 x 2.2 = 3.3 pounds
- 2.25 pounds of cheese = 2.25 pounds
Therefore, Roger purchased more turkey.
To find the amount in pounds that the chicken could weigh, we need to find a weight that is greater than the beef weight (1.25 pounds) and less than the turkey weight (3.3 pounds).
Let's use the average between the two:
(1.25 + 3.3) / 2 = 2.275
Therefore, the chicken could weigh approximately 2.28 pounds.
To determine if the total weight of the sandwich fillings will be a greater number of ounces or a greater number of grams, we need to convert the weights into both units and compare.
1. Convert the weights given into ounces:
- 1.5 kilograms of turkey = 1.5 x 1000 / 28.35 = 52.96 ounces
- 1.25 kilograms of beef = 1.25 x 1000 / 28.35 = 44.05 ounces
- 2.25 pounds of cheese = 2.25 x 16 = 36 ounces
2. Convert the weights given into grams:
- 1.5 kilograms of turkey = 1.5 x 1000 = 1500 grams
- 1.25 kilograms of beef = 1.25 x 1000 = 1250 grams
- 2.25 pounds of cheese = 2.25 x 453.59 = 1021.27 grams
Comparing the weights, we can see that the total weight of the sandwich fillings will be a greater number of grams since the grams conversion results in higher values.