Question 1:
To determine which board Mia will use for the length of the shelter, we need to find the board that is closest to 3.25 feet.
The measurements of the boards are:
36 inches = 3 feet
39 inches = 3.25 feet
42 inches = 3.5 feet
Therefore, Mia will use the 39-inch board for the length of the shelter.
The width of the shelter will be shorter than the length. However, the width of the shelter is not given in feet, so we cannot determine the exact measurement without additional information.
To find how many feet of the third board Mia needs to cut off to match the width of the shelter, we need to know the desired width of the shelter in feet. Since this information is missing, we cannot determine the answer.
Question 2:
To determine which board, if any, will cover all the space needed for the roof, we need to compare the areas of the boards.
The board that measures 1 square yard has an area of 1 yard × 1 yard = 1 square yard.
The second board measures 3 feet × 3 feet = 9 square feet.
The third board measures 36 inches × 36 inches = 1296 square inches ÷ 12 inches = 108 square feet.
Comparing the areas:
1 square yard = 9 square feet
1 square yard < 9 square feet
Therefore, the board that measures 1 square yard will not cover all the space needed for the roof.
Answer: None of the boards will cover all the space needed for the roof.
Question 1 (from the conversion portfolio):
To determine if Roger can use the 8-liter bowl to mix all the ingredients for the punch, we need to convert the quantities of the ingredients into liters.
2 quarts orange juice = 2 quarts × 1.06 liters per quart = 2.12 liters
3 cups cranberry juice = 3 cups × 0.24 liters per cup = 0.72 liters
1 gallon ginger ale = 1 gallon × 3.79 liters per gallon = 3.79 liters
1 pint pineapple juice = 1 pint × 0.47 liters per pint = 0.47 liters
Total volume of ingredients = 2.12 liters + 0.72 liters + 3.79 liters + 0.47 liters = 7.1 liters
Since the total volume of the ingredients is less than 8 liters, Roger can use the 8-liter bowl to mix all the ingredients for the punch.
The amount of liquid that could still fit into the bowl is 8 liters - 7.1 liters = 0.9 liters.
Question 2:
To determine whether Roger purchased more turkey or more cheese, we need to compare the weights of turkey and cheese in the same unit.
1.5 kilograms of turkey = 1.5 kilograms × 2.2 pounds per kilogram = 3.3 pounds
2.25 pounds of cheese = 2.25 pounds
Since 3.3 pounds > 2.25 pounds, Roger purchased more turkey than cheese.
To find the amount in pounds that the chicken could weigh, we know it must be more than 1.25 kilograms (weight of beef) and less than 1.5 kilograms (weight of turkey).
1.25 kilograms × 2.2 pounds per kilogram = 2.75 pounds
1.5 kilograms × 2.2 pounds per kilogram = 3.3 pounds
Therefore, the chicken could weigh between 2.75 pounds and 3.3 pounds, rounded to the nearest hundredth of a pound.
To determine the total weight of all four sandwich fillings using ounces and grams, we need to convert the weights of the fillings to the same unit.
1.5 kilograms of turkey = 1.5 kilograms × 1000 grams per kilogram × 0.035 ounces per gram ≈ 52.92 ounces
1.25 kilograms of beef = 1.25 kilograms × 1000 grams per kilogram × 0.035 ounces per gram ≈ 43.75 ounces
2.25 pounds of cheese = 2.25 pounds × 16 ounces per pound ≈ 36 ounces
Total weight in ounces = 52.92 ounces + 43.75 ounces + 36 ounces = 132.67 ounces
Total weight in grams = 1.5 kilograms × 1000 grams per kilogram + 1.25 kilograms × 1000 grams per kilogram + 2.25 pounds × 453.59 grams per pound ≈ 5025.65 grams
Since 16 ounces = 1 pound and 1,000 grams = 1 kilogram, the total weight in ounces is greater than the total weight in grams.
Mia is building a three-sided shelter for her action figures. The shelter will
resemble a rectangle with one of the long sides removed. She has boards that
measure 36 inches, 39 inches, and 42 inches in length; all the boards are the
same width. Mia will need to convert some of these measurements into other
imperial units to build the shelter the way she wants. Answer the following
questions. Show your work. Record your answers below.
Question 1
Mia will use one of these boards for the length of the shelter. She knows she wants
the length of the shelter to measure 3.25 feet. She will use a different board for the
width of the shelter. The width of the shelter will be shorter than the length.
Which board will Mia use for the length of the shelter, given that 1 foot = 12 inches?
What is the width of the shelter, measured in feet?
Mia needs to cut the third board to match the width of the shelter. How many feet of
board will she need to cut off the existing board to reach this goal?
Question 2
For the roof of the shelter, Mia has a board that measures 1 square yard, a second
board that measures 3 feet by 3 feet, and a third board that measures 36 inches by
36 inches. Which of these, if any, will cover all the space needed for the roof?
Explain your answer, drawing a picture if necessary.
1 foot = 1/3 of a yard
Converting Between Systems Portfolio
Use what you have learned about converting between metric and imperial
measurements to answer the questions.
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 oun
2 answers
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
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
1 answer