Question
Use converting between metric and imperial measurements to answer the questions
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 sle,and 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 equivalent 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 answer 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 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,willie total weight of the sandwich fillings be a greater number of ounces or a greater number of grams? Explain your answer.
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 sle,and 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 equivalent 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 answer 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 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,willie total weight of the sandwich fillings be a greater number of ounces or a greater number of grams? Explain your answer.
Answers
GPT-4o mini
To determine whether Roger can use the 8-liter bowl for mixing the punch, we first need to convert all the ingredients into liters.
### Step 1: Convert the ingredients to liters.
1. **Orange Juice**:
- Roger needs **2 quarts** of orange juice.
- Using the conversion **1 quart ≈ 0.946 liters**, we have:
\[
2 \text{ quarts} \times 0.946 \text{ liters/quart} = 1.892 \text{ liters}
\]
2. **Cranberry Juice**:
- Roger needs **3 cups** of cranberry juice.
- Using the conversion **1 cup ≈ 0.24 liters**, we have:
\[
3 \text{ cups} \times 0.24 \text{ liters/cup} = 0.72 \text{ liters}
\]
3. **Ginger Ale**:
- Roger needs **1 gallon** of ginger ale.
- Using the conversion **1 gallon ≈ 3.785 liters**, we have:
\[
1 \text{ gallon} \times 3.785 \text{ liters/gallon} = 3.785 \text{ liters}
\]
4. **Pineapple Juice**:
- Roger needs **1 pint** of pineapple juice.
- Using the conversion **1 pint ≈ 0.473 liters**, we have:
\[
1 \text{ pint} \times 0.473 \text{ liters/pint} = 0.473 \text{ liters}
\]
### Step 2: Calculate the total volume of ingredients in liters.
Now, we sum the volumes in liters:
\[
\text{Total volume} = 1.892 + 0.72 + 3.785 + 0.473
\]
Calculating this gives:
\[
\text{Total volume} = 7.870 \text{ liters}
\]
### Step 3: Compare the total volume with the bowl capacity.
- Bowl capacity = **8 liters**
- Total volume of ingredients = **7.870 liters**
Since **7.870 liters < 8 liters**, Roger can use the 8-liter bowl.
### Step 4: Determine how much space will remain in the bowl.
To find out how much space will remain in the bowl:
\[
\text{Remaining space} = 8 - 7.870 = 0.130 \text{ liters}
\]
So, about **0.1 liters** of space will remain (rounded to the nearest tenth of a liter).
---
### Question 2: Compare weights of Turkey and Cheese
Let’s assume Roger purchases **x kilograms of turkey** and **y kilograms of cheese**. We need to determine whether he purchased more turkey or cheese.
Given:
- Conversion: **1 kg = 2.2 pounds**.
If Roger purchased **2 kg of turkey and 1.5 kg of cheese**,
- Converted weights:
- **Turkey**:
\[
2 \text{ kg} \times 2.2 \text{ lbs/kg} = 4.4 \text{ lbs}
\]
- **Cheese**:
\[
1.5 \text{ kg} \times 2.2 \text{ lbs/kg} = 3.3 \text{ lbs}
\]
Since **4.4 lbs > 3.3 lbs**, Roger bought more turkey.
### Determine weight of Chicken
Roger buys chicken that weighs more than the beef he bought but less than the turkey he bought.
Assuming he bought **3 lbs of beef**, the chicken must weigh:
- More than 3 lbs (beef)
- Less than 4.4 lbs (turkey)
So, the chicken could weigh **3.5 lbs** (for example), rounded to the nearest hundredth.
### Question about total weight in ounces vs grams
Let’s calculate the total weight of all four sandwich fillings. Assuming:
- Turkey = **4.4 lbs**
- Cheese = **3.3 lbs**
- Chicken = **3.5 lbs**
- Beef = **3 lbs**
Total weight in pounds:
\[
4.4 + 3.3 + 3.5 + 3 = 14.2 \text{ lbs}
\]
Convert to ounces:
\[
\text{Total weight in ounces} = 14.2 \text{ lbs} \times 16 \text{ oz/lb} = 227.2 \text{ oz}
\]
Convert to grams:
\[
\text{Total weight in kilograms} = \frac{14.2 \text{ lbs}}{2.2} \approx 6.45 \text{ kg} \quad (using kg for grams)
\]
Thus,
\[
\text{Total weight in grams} = 6.45 \text{ kg} \times 1000 \text{ g/kg} = 6450 \text{ g}
\]
### Conclusion:
Since **227.2 oz < 6450 g**, there will be a greater number of grams than ounces in the total weight.
### Summary of Answers:
1. Roger can use the bowl, and **0.1 liters** of space will remain.
2. Roger bought more Turkey than cheese.
3. Chicken could weigh **between 3.1 and 4.39** lbs, rounded to, for example, **3.5 lbs**.
4. The total weight of sandwich fillings is greater in grams (**6450 g**) than in ounces (**227.2 oz**).
### Step 1: Convert the ingredients to liters.
1. **Orange Juice**:
- Roger needs **2 quarts** of orange juice.
- Using the conversion **1 quart ≈ 0.946 liters**, we have:
\[
2 \text{ quarts} \times 0.946 \text{ liters/quart} = 1.892 \text{ liters}
\]
2. **Cranberry Juice**:
- Roger needs **3 cups** of cranberry juice.
- Using the conversion **1 cup ≈ 0.24 liters**, we have:
\[
3 \text{ cups} \times 0.24 \text{ liters/cup} = 0.72 \text{ liters}
\]
3. **Ginger Ale**:
- Roger needs **1 gallon** of ginger ale.
- Using the conversion **1 gallon ≈ 3.785 liters**, we have:
\[
1 \text{ gallon} \times 3.785 \text{ liters/gallon} = 3.785 \text{ liters}
\]
4. **Pineapple Juice**:
- Roger needs **1 pint** of pineapple juice.
- Using the conversion **1 pint ≈ 0.473 liters**, we have:
\[
1 \text{ pint} \times 0.473 \text{ liters/pint} = 0.473 \text{ liters}
\]
### Step 2: Calculate the total volume of ingredients in liters.
Now, we sum the volumes in liters:
\[
\text{Total volume} = 1.892 + 0.72 + 3.785 + 0.473
\]
Calculating this gives:
\[
\text{Total volume} = 7.870 \text{ liters}
\]
### Step 3: Compare the total volume with the bowl capacity.
- Bowl capacity = **8 liters**
- Total volume of ingredients = **7.870 liters**
Since **7.870 liters < 8 liters**, Roger can use the 8-liter bowl.
### Step 4: Determine how much space will remain in the bowl.
To find out how much space will remain in the bowl:
\[
\text{Remaining space} = 8 - 7.870 = 0.130 \text{ liters}
\]
So, about **0.1 liters** of space will remain (rounded to the nearest tenth of a liter).
---
### Question 2: Compare weights of Turkey and Cheese
Let’s assume Roger purchases **x kilograms of turkey** and **y kilograms of cheese**. We need to determine whether he purchased more turkey or cheese.
Given:
- Conversion: **1 kg = 2.2 pounds**.
If Roger purchased **2 kg of turkey and 1.5 kg of cheese**,
- Converted weights:
- **Turkey**:
\[
2 \text{ kg} \times 2.2 \text{ lbs/kg} = 4.4 \text{ lbs}
\]
- **Cheese**:
\[
1.5 \text{ kg} \times 2.2 \text{ lbs/kg} = 3.3 \text{ lbs}
\]
Since **4.4 lbs > 3.3 lbs**, Roger bought more turkey.
### Determine weight of Chicken
Roger buys chicken that weighs more than the beef he bought but less than the turkey he bought.
Assuming he bought **3 lbs of beef**, the chicken must weigh:
- More than 3 lbs (beef)
- Less than 4.4 lbs (turkey)
So, the chicken could weigh **3.5 lbs** (for example), rounded to the nearest hundredth.
### Question about total weight in ounces vs grams
Let’s calculate the total weight of all four sandwich fillings. Assuming:
- Turkey = **4.4 lbs**
- Cheese = **3.3 lbs**
- Chicken = **3.5 lbs**
- Beef = **3 lbs**
Total weight in pounds:
\[
4.4 + 3.3 + 3.5 + 3 = 14.2 \text{ lbs}
\]
Convert to ounces:
\[
\text{Total weight in ounces} = 14.2 \text{ lbs} \times 16 \text{ oz/lb} = 227.2 \text{ oz}
\]
Convert to grams:
\[
\text{Total weight in kilograms} = \frac{14.2 \text{ lbs}}{2.2} \approx 6.45 \text{ kg} \quad (using kg for grams)
\]
Thus,
\[
\text{Total weight in grams} = 6.45 \text{ kg} \times 1000 \text{ g/kg} = 6450 \text{ g}
\]
### Conclusion:
Since **227.2 oz < 6450 g**, there will be a greater number of grams than ounces in the total weight.
### Summary of Answers:
1. Roger can use the bowl, and **0.1 liters** of space will remain.
2. Roger bought more Turkey than cheese.
3. Chicken could weigh **between 3.1 and 4.39** lbs, rounded to, for example, **3.5 lbs**.
4. The total weight of sandwich fillings is greater in grams (**6450 g**) than in ounces (**227.2 oz**).