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To determine if Roger can fit all the ingredients into an 8-liter bowl, we first need to convert all the ingredients into liters using the provided measurement equivalents.

Ingredient quantities:

Orange juice: 2 quarts
Cranberry juice: 3 cups
Ginger ale: 1 gallon
Pineapple juice: 1 pint
Step 1: Convert each ingredient to liters.

Orange juice (2 quarts):

Conversion: 1 quart ≈ 0.946 liters
Cranberry juice (3 cups):

Conversion: 1 liter ≈ 4.23 cups

Ginger ale (1 gallon):

Conversion: 1 gallon ≈ 3.785 liters
Pineapple juice (1 pint):

Conversion: 1 pint ≈ 0.473 liters
Step 2: Add up all the converted amounts.

Calculating the total:

Step 3: Compare with the bowl's capacity (8 liters).

Since
, Roger can use the bowl.

Step 4: Calculate how much space will be left in the bowl.

Final Answer: Roger can use the 8-liter bowl, and there will be approximately 0.1 liters of extra space left in the bowl. please make your answer short

7 answers

Let's convert each ingredient to liters:

  1. Orange juice: \(2 \text{ quarts} \times 0.946 \text{ liters/quart} \approx 1.892 \text{ liters}\)

  2. Cranberry juice: \(3 \text{ cups} \div 4.23 \text{ cups/liter} \approx 0.708 \text{ liters}\)

  3. Ginger ale: \(1 \text{ gallon} \approx 3.785 \text{ liters}\)

  4. Pineapple juice: \(1 \text{ pint} \approx 0.473 \text{ liters}\)

Total volume: \[ 1.892 + 0.708 + 3.785 + 0.473 \approx 7.858 \text{ liters} \]

Comparison with bowl's capacity: \[ 8 \text{ liters} - 7.858 \text{ liters} \approx 0.142 \text{ liters} \]

Final Answer: Roger can use the 8-liter bowl, and there will be approximately 0.142 liters of extra space left in the bowl.

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. keep your answer short

To determine if Roger purchased more turkey or cheese, we need to convert the turkey into pounds.

  1. Turkey: \[ 1.5 \text{ kg} \times 2.2 \text{ lbs/kg} = 3.3 \text{ lbs} \]

  2. Cheese: \[ 2.25 \text{ lbs} \quad (\text{already in pounds}) \]

Comparison:

  • Turkey: 3.3 lbs
  • Cheese: 2.25 lbs

Conclusion: Roger purchased more turkey (3.3 lbs) than cheese (2.25 lbs).

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. keep your answer short

Roger bought 1.25 kilograms of beef, which is approximately: \[ 1.25 \text{ kg} \times 2.2 \text{ lbs/kg} = 2.75 \text{ lbs} \] He bought 1.5 kilograms of turkey, which is approximately: \[ 1.5 \text{ kg} \times 2.2 \text{ lbs/kg} = 3.3 \text{ lbs} \]

The chicken must weigh more than 2.75 lbs but less than 3.3 lbs.

A possible weight for the chicken could be: 3.00 lbs (rounded to the nearest hundredth).

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 grams? explain your answer

Let's first convert the weights of all the sandwich fillings into pounds and then into ounces and grams.

  1. Turkey: 1.5 kilograms \[ 1.5 \text{ kg} \times 2.2 \text{ lbs/kg} = 3.3 \text{ lbs} \] \[ 3.3 \text{ lbs} \times 16 \text{ oz/lb} = 52.8 \text{ oz} \]

  2. Beef: 1.25 kilograms \[ 1.25 \text{ kg} \times 2.2 \text{ lbs/kg} = 2.75 \text{ lbs} \] \[ 2.75 \text{ lbs} \times 16 \text{ oz/lb} = 44.0 \text{ oz} \]

  3. Cheese: 2.25 pounds \[ 2.25 \text{ lbs} \times 16 \text{ oz/lb} = 36.0 \text{ oz} \]

  4. Chicken: To satisfy the previous conditions, let’s use a reasonable weight for chicken. Assuming we choose 3.0 pounds for chicken: \[ 3.0 \text{ lbs} \times 16 \text{ oz/lb} = 48.0 \text{ oz} \]

Now, we sum the weights in pounds: \[ 3.3 + 2.75 + 2.25 + 3.0 = 11.3 \text{ lbs} \]

Convert total weight to ounces:

\[ 11.3 \text{ lbs} \times 16 \text{ oz/lb} = 180.8 \text{ oz} \]

Convert total weight to grams:

  1. Convert the total weight in kilograms: \[ 11.3 \text{ lbs} \div 2.2 \text{ lbs/kg} \approx 5.136 \text{ kg} \]

  2. Convert to grams: \[ 5.136 \text{ kg} \times 1000 \text{ g/kg} = 5136 \text{ g} \]

Conclusion:

  • Total weight in ounces: 180.8 oz
  • Total weight in grams: 5136 g

To compare:

  • 1 ounce is approximately 28.35 grams.
  • The total weight in ounces (180.8 oz) converted to grams: \[ 180.8 \text{ oz} \times 28.35 \text{ g/oz} \approx 5125.88 \text{ g} \]

Since \(5136 \text{ g} > 5125.88 \text{ g}\), the total weight in grams (5136 g) is greater than the total weight in ounces (180.8 oz).

Final Answer: The total weight of the sandwich fillings will be a greater number of grams than ounces.