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?
To find out which board Mia will use for the length of the shelter, we need to convert the desired length of the shelter to inches. We know that 1 foot is equal to 12 inches, so to convert 3.25 feet to inches, we multiply by 12:
3.25 feet * 12 inches/foot = 39 inches
So, Mia will use the board that measures 39 inches for the length of the shelter.
Next, we need to find out the width of the shelter. Since Mia wants the width to be shorter than the length, she will use the board that is shorter than 39 inches for the width. We know that the other two boards measure 36 inches and 42 inches. Therefore, the board that measures 36 inches will be used for the width of the shelter.
To find the width of the shelter in feet, we need to convert 36 inches to feet. Again, using the conversion factor of 1 foot = 12 inches, we divide 36 inches by 12:
36 inches / 12 inches/foot = 3 feet
So, the width of the shelter is 3 feet.
Finally, Mia needs to cut the third board (the one that measures 42 inches) to match the width of the shelter, which is 3 feet. We need to find out how many feet Mia will need to cut off.
To do this, we first convert the desired width from feet to inches:
3 feet * 12 inches/foot = 36 inches
Then, we subtract this from the length of the existing board:
42 inches - 36 inches = 6 inches
To convert this to feet, we divide by 12:
6 inches / 12 inches/feet = 0.5 feet
Therefore, Mia will need to cut off 0.5 feet or 6 inches from the existing board to reach her goal.
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
To determine which board will cover all the space needed for the roof, we need to calculate the area of the roof and compare it to the area of each board.
First, let's convert all the measurements to the same units. We know that 1 foot is equal to 1/3 of a yard, so 3 feet is equal to 1 yard. Therefore, the second board, which measures 3 feet by 3 feet, is equivalent to 1 yard by 1 yard.
Now, let's calculate the area of each board:
- The first board measures 1 square yard, so its area is 1 yard * 1 yard = 1 square yard.
- The second board measures 1 yard * 1 yard = 1 square yard.
- The third board measures 36 inches * 36 inches. To convert inches to yards, we divide by 36 (since 1 yard is equal to 36 inches). So, the area of the third board is (36 inches / 36 inches/yard) * (36 inches / 36 inches/yard) = 1 yard * 1 yard = 1 square yard.
From our calculations, all three boards have the same area of 1 square yard. Therefore, any of the three boards will cover all the space needed for the roof of the shelter.
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 for the punch, we need to convert the quantities of each ingredient to liters and see if the total fits within 8 liters.
- 2 quarts orange juice = 2 quarts * 1.06 liters/quart = 2.12 liters
- 3 cups cranberry juice = 3 cups * 0.24 liters/cup = 0.72 liters
- 1 gallon ginger ale = 1 gallon * 3.79 liters/gallon = 3.79 liters
- 1 pint pineapple juice = 1 pint * 0.47 liters/pint = 0.47 liters
Now, let's calculate the total volume of the ingredients:
2.12 liters + 0.72 liters + 3.79 liters + 0.47 liters = 7.1 liters
The total volume of the ingredients is 7.1 liters, which is less than the capacity of the 8-liter bowl. Therefore, Roger can use the bowl to mix all the ingredients for the punch.
To determine how many liters of liquid could still fit into the bowl, we subtract the total volume of the ingredients from the capacity of the bowl:
8 liters - 7.1 liters = 0.9 liters
Therefore, Roger could fit 0.9 liters of additional liquid into the bowl.
Question 2:
To determine whether Roger purchased more turkey or more cheese, we need to convert their weights to the same unit.
- 1.5 kilograms of turkey = 1.5 kilograms * 2.2 pounds/kilogram = 3.3 pounds
- 2.25 pounds of cheese = 2.25 pounds
Roger purchased 3.3 pounds of turkey and 2.25 pounds of cheese. Therefore, he purchased more turkey than cheese.
For the weight of the chicken, we know that it weighs more than the beef (1.25 kilograms = 2.75 pounds) and less than the turkey (1.5 kilograms = 3.3 pounds). Therefore, the weight of the chicken could be between 2.75 pounds and 3.3 pounds, rounded to the nearest hundredth of a pound.
To determine whether the total weight of the sandwich fillings will be a greater number of ounces or kilograms, we need to consider the conversion factors.
- 1 pound = 16 ounces
- 1 kilogram = 1,000 grams = 2.2 pounds
Since 16 ounces is equal to 1 pound, the total weight in ounces will always be greater than or equal to the total weight in pounds. Similarly, since 1,000 grams is equal to 2.2 pounds, the total weight in kilograms will always be less than or equal to the total weight in pounds. Therefore, the total weight of the sandwich fillings will be a greater number of ounces.
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 provided in the question, so we cannot determine the exact cost.
Let's assume the cost of the board game is $15.
Now, let's choose a state from the given options. Suppose we choose Tennessee.
The general sales tax rate in Tennessee is 7%.
To calculate the total cost of the board game, including sales tax, we need to add the sales tax amount to the cost of the game.
Sales tax amount = cost of the game * sales tax rate
Sales tax amount = $15 * 0.07 = $1.05
Total cost of the board game = cost of the game + sales tax amount
Total cost of the board game = $15 + $1.05 = $16.05
Therefore, if the cost of the board game is $15 and we are in Tennessee with a sales tax rate of 7%, the total cost of the board game, including sales tax, would be $16.05.