Question 1
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
Question 2
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.
Roger is curious to know the total weight of all four sandwich fillings he bought. He
weighs it 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 kilograms? Explain your answer
Question 1:
To determine if Roger can use the 8-liter bowl to mix all the ingredients, we need to convert the quantities of each ingredient to liters.
To do this, we'll use the measurement equivalents provided:
1 liter = 4.23 cups
1 liter = 2.11 pints
1 liter = 1.06 quarts
1 liter = 0.26 gallons
The quantities of each ingredient in liters are:
2 quarts orange juice = 2 * 1.06 = 2.12 liters
3 cups cranberry juice = 3 * 4.23 / 4 = 3.18 liters
1 gallon ginger ale = 1 * 3.78 = 3.78 liters
1 pint pineapple juice = 1 * 2.11 / 2 = 1.06 liters
The total quantity of all the ingredients is:
2.12 + 3.18 + 3.78 + 1.06 = 10.14 liters
Since 10.14 liters is greater than the capacity of the bowl (8 liters), Roger cannot fit all the ingredients in the bowl at the same time.
To determine how many extra liters of liquid there are, we subtract the capacity of the bowl from the total quantity of the ingredients:
10.14 - 8 = 2.14 liters
Therefore, Roger has 2.14 liters of extra liquid.
Question 2:
To determine if Roger purchased more turkey or more cheese, we need to convert the quantities to the same unit of measurement.
1.5 kilograms of turkey = 1.5 * 2.2 = 3.3 pounds
2.25 pounds of cheese = 2.25 pounds
Since 3.3 pounds is greater than 2.25 pounds, Roger purchased more turkey than cheese.
To find the weight of the chicken that weighs more than the beef but less than the turkey, we know that it must be between 2.25 pounds and 3.3 pounds. Unfortunately, the specific weight cannot be determined without more information.
To determine if the total weight of the sandwich fillings will be a greater number of ounces or a greater number of kilograms, we need to convert the weights of the fillings to the same unit of measurement.
1 pound = 16 ounces
1 kilogram = 1000 grams
The weight of the turkey, beef, and cheese in kilograms is:
1.5 kilograms of turkey
1.25 kilograms of beef
To convert the weight of cheese from pounds to kilograms, we'll use the conversion ratio:
2.25 pounds of cheese = 2.25 / 2.2 ≈ 1.02 kilograms
The weight of the turkey, beef, and cheese in ounces is:
3.3 pounds of turkey = 3.3 * 16 = 52.8 ounces
1.25 kilograms of beef = 1.25 * 2.2 * 16 ≈ 43.55 ounces
2.25 pounds of cheese = 2.25 * 16 ≈ 36 ounces
Comparing the weights, we can see that the total weight of the sandwich fillings is a greater number of ounces (52.8 + 43.55 + 36 = 132.35 ounces) compared to kilograms (1.02 + 1.5 + 1.25 = 3.77 kilograms).
Therefore, the total weight of the sandwich fillings is a greater number of ounces.
For Question 1:
To determine if Roger can fit all the punch ingredients in the 8-liter bowl, let's convert each ingredient quantity to liters:
1 quart is equivalent to 0.946 liters (rounding to the nearest tenth)
2 quarts of orange juice is 2 * 0.946 = 1.892 liters
1 cup is equivalent to 0.236 liters (rounding to the nearest tenth)
3 cups of cranberry juice is 3 * 0.236 = 0.708 liters
1 gallon is equivalent to 3.785 liters (rounding to the nearest tenth)
1 gallon of ginger ale is 1 * 3.785 = 3.785 liters
1 pint is equivalent to 0.473 liters (rounding to the nearest tenth)
1 pint of pineapple juice is 1 * 0.473 = 0.473 liters
Now, let's find the total quantity of the ingredients in liters:
Total = 1.892 + 0.708 + 3.785 + 0.473 = 6.858 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. The amount of extra space in the bowl would be the difference between the bowl capacity and the total quantity of the ingredients:
Extra space = 8 - 6.858 = 1.142 liters
Therefore, Roger can use the 8-liter bowl to mix all the ingredients, and there would be approximately 1.1 liters of extra space.
For Question 2:
To determine if Roger purchased more turkey or more cheese, let's convert both quantities to pounds:
1 kilogram is equivalent to 2.2 pounds
1.5 kilograms of turkey is 1.5 * 2.2 = 3.3 pounds
1.25 kilograms of beef remains in kilograms because we're comparing it to other quantities
To compare the weights, let's convert the cheese quantity to kilograms:
2.25 pounds is equivalent to 2.25 / 2.2 = 1.0227 kilograms
Therefore, Roger purchased more turkey (3.3 pounds) than cheese (1.02 kilograms).
As for the weight of the chicken, since it weighs more than the beef and less than the turkey, it could be any amount between 1.25 kilograms and 1.5 kilograms, which is between 2.75 pounds and 3.3 pounds. Rounding to the nearest hundredth of a pound, the chicken could weigh between 2.75 pounds and 3.30 pounds.
For the final question, the weight of the sandwich fillings will be a greater number of kilograms. This is because 1 kilogram is equivalent to 1,000 grams, which is a larger unit of weight compared to 16 ounces, where 1 pound is equivalent to 16 ounces. Therefore, the weight in kilograms will be greater than the weight in ounces.
Question 1:
To determine if Roger can fit all the ingredients in the 8-liter bowl, we need to convert the given quantities of orange juice, cranberry juice, ginger ale, and pineapple juice to liters.
Given:
1 liter is about 4.23 cups
1 liter is about 2.11 pints
1 liter is about 1.06 quarts
1 liter is about 0.26 gallons
Let's convert the quantities of each ingredient to liters:
2 quarts of orange juice = 2 x 1.06 = 2.12 liters
3 cups of cranberry juice = 3 x 4.23 / 8.46 liters
1 gallon of ginger ale = 1 x 3.78 liters
1 pint of pineapple juice = 1 x 2.11 / 2.12 liters
Now, let's add up the quantities to get the total volume of the ingredients in liters:
2.12 + (3 x 4.23 / 8.46) + 3.78 + (1 x 2.11 / 2.12) = total volume in liters
Once we have the total volume, we can compare it to the capacity of the 8-liter bowl. If the total volume is less than or equal to 8 liters, Roger can use the bowl. If it is greater, he cannot use the bowl.
To determine how many liters of liquid could still fit into the bowl if Roger can use it, we subtract the total volume from the capacity of the bowl (i.e., 8 liters - total volume).
Question 2:
To determine if Roger purchased more turkey or more cheese, we need to convert the given quantities of turkey and cheese to the same unit (pounds).
Given:
1 kilogram is about 2.2 pounds
Let's convert the quantities of turkey and cheese to pounds:
1.5 kilograms of turkey = 1.5 x 2.2 pounds
2.25 pounds of cheese = 2.25 pounds
Now we can compare the quantities to see if Roger purchased more turkey or more cheese by simply comparing the values.
For the third part of the question, to find the amount in pounds that the chicken could weigh, we know it is more than the beef (1.25 kilograms) and less than the turkey (1.5 kilograms). So the weight of the chicken falls within the range of 1.25 to 1.5 kilograms.
To convert this range to pounds, we multiply the range (1.25 to 1.5) by the conversion factor (2.2 pounds per kilogram) to get the range in pounds.
Finally, for the last question, we need to compare the total weight of the sandwich fillings in ounces and grams.
Given:
16 ounces = 1 pound
1000 grams = 1 kilogram
We need to convert the total weight of the sandwich fillings in ounces and grams to determine which is greater.
You are visiting one of the following states: Tennessee, Vermont, Wisconsin, or
Wyoming. Each has a state sales tax on most items that are for sale in stores.
While you are visiting, you decide to buy a board game to play with your hosts. The
cost of the game is between $10 and $20, and it is not a whole dollar amount.
Decide the cost of the board game. Write it here: ______
Now choose one of the four states listed above. Write it here: __________________
Use the internet to find the state’s general sales tax. Note that some counties, towns,
or cities may add more to the general sales tax, but you only need the general sales
tax. Write the tax rate here: ________
What is the total cost of the board game, including sales tax? Show your work
The cost of the board game is not given in the question, so I cannot fill in the blank with a specific amount.
Let's assume the cost of the board game is $15.
The chosen state is not mentioned in the question, so I cannot fill in the blank with a specific state.
Let's assume the chosen state is Vermont.
Using the internet, I found that the general sales tax rate in Vermont is 6%.
To find the total cost of the board game including sales tax, we need to add the sales tax amount to the cost of the board game.
Sales tax amount = cost of the board game * sales tax rate / 100
Sales tax amount = 15 * 6 / 100 = 0.9
Total cost of the board game including sales tax = cost of the board game + sales tax amount
Total cost of the board game including sales tax = 15 + 0.9 = 15.9
Therefore, the total cost of the board game, including sales tax in Vermont, is $15.9.