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 the boards, 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
make it easy
Let's compare the sizes of the three boards Mia has to cover the roof of the shelter.
1. The first board measures 1 square yard.
2. The second board measures 3 feet by 3 feet.
3. The third board measures 36 inches by 36 inches.
To easily compare these measurements, we can convert them all into the same unit. Given that 1 yard equals 3 feet, and 1 foot equals 12 inches, we can make the following conversions:
1 square yard is equivalent to:
- 1 yard * 3 feet/yard = 3 feet on one side
- So, 3 feet * 3 feet = 9 square feet
The second board measures 3 feet by 3 feet, which is:
- 3 feet * 3 feet = 9 square feet (Same as above.)
The third board measures 36 inches by 36 inches. Since there are 12 inches in a foot, the board in feet is:
- 36 inches / 12 inches/foot = 3 feet on one side
- So, 3 feet * 3 feet = 9 square feet (Again, the same as above.)
After converting, we see that all three boards are indeed the same size when their dimensions are converted into the same units. Each board measures 3 feet by 3 feet, corresponding to 9 square feet, or 1 square yard when heights and widths are considered.
Thus, any of the boards will cover the same area of space needed for the roof, and it comes down to Mia's preference for which material to use based on other factors, such as thickness, weight, or ease of use.
make it shorter
All three boards that Mia has are equivalent in size because they all measure 3 feet by 3 feet, which is also the same as 1 square yard or 36 inches by 36 inches. Converting all the dimensions to the same unit, we find that each board will cover 9 square feet (or 1 square yard) of space. Therefore, any of the boards can be used to cover the space needed for the roof.
shorter
All three boards are the same size: 1 square yard, 3 feet by 3 feet, and 36 inches by 36 inches are different ways to describe the same area. Any board will cover the roof space needed, as they are all equivalent in size.
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. 1 liter is about 4.23 cups, 2.11 pints,
1.06 quarts, and 0.26 gallons. Show your work.
First, let's convert all the ingredients Roger needs for the punch into one common unit. We'll choose liters for consistency, and we'll use the given measurement equivalents for the conversion.
Ingredients:
1. 2 quarts of orange juice
2. 3 cups of cranberry juice
3. 1 gallon of ginger ale
4. 1 pint of pineapple juice
Conversions (using the given equivalents):
- 1 quart is approximately 1.06 liters.
- 1 cup is approximately 1/4.23 liters.
- 1 gallon is approximately 3.785 liters (since 1 gallon = 4 quarts and 1 quart ≈ 1.06 liters).
- 1 pint is approximately 2.11 pints per liter.
Now let's calculate:
1. Orange juice: 2 quarts × 1.06 liters/quart = 2.12 liters.
2. Cranberry juice: 3 cups × (1/4.23 liters/cup) ≈ 3 / 4.23 liters ≈ 0.71 liters.
3. Ginger ale: 1 gallon × 3.785 liters/gallon = 3.785 liters.
4. Pineapple juice: 1 pint × (1/2.11 pints/liter) = 1 / 2.11 liters ≈ 0.47 liters.
Finally, let’s add up all the ingredients in liters:
2.12 liters (orange juice) + 0.71 liters (cranberry juice) + 3.785 liters (ginger ale) + 0.47 liters (pineapple juice) = 7.085 liters total.
Since 7.085 liters is less than the 8 liters capacity of the bowl, Roger can indeed use the bowl to mix all of the ingredients for the punch at the same time.
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.
In the previous explanation, we calculated the total volume of the punch ingredients in liters as 7.085 liters. Roger has a bowl that holds 8 liters. Now we'll determine how much more liquid can fit into the bowl by subtracting the total volume of the punch ingredients from the bowl's capacity.
Bowl capacity - Total volume of ingredients = Remaining volume
8 liters (bowl capacity) - 7.085 liters (total punch ingredients) ≈ 0.915 liters
Now we'll round this to the nearest tenth of a liter:
0.915 liters ≈ 0.9 liters
So, after combining all the punch ingredients, the bowl will still be able to hold about 0.9 liters of additional liquid.
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
a. 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.