Question

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.

Answer 1

shorter

Answer 2

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.
keep your answer short

Answer 3

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

Answer 4

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? keep your answer short

Answer 5

To determine whether Roger can fit all the ingredients for the punch into an 8-liter bowl, we need to convert the quantities of each ingredient to liters using the provided measurement equivalents.

### Step 1: Convert each ingredient to liters.

1. **Orange Juice:**
\[
2 \text{ quarts} \times \frac{1.06 \text{ liters}}{1 \text{ quart}} = 2.12 \text{ liters}
\]

2. **Cranberry Juice:**
\[
3 \text{ cups} \times \frac{1 \text{ liter}}{4.23 \text{ cups}} \approx 0.709 \text{ liters}
\]

3. **Ginger Ale:**
\[
1 \text{ gallon} \times \frac{1 \text{ liter}}{0.26 \text{ gallons}} \approx 3.85 \text{ liters}
\]

4. **Pineapple Juice:**
\[
1 \text{ pint} \times \frac{1 \text{ liter}}{2.11 \text{ pints}} \approx 0.474 \text{ liters}
\]

### Step 2: Sum the converted quantities

Now we will sum all the converted quantities in liters:
\[
\text{Total Volume} = \text{Orange Juice} + \text{Cranberry Juice} + \text{Ginger Ale} + \text{Pineapple Juice}
\]
\[
\text{Total Volume} = 2.12 + 0.709 + 3.85 + 0.474 \approx 7.153 \text{ liters}
\]

### Step 3: Compare total volume to bowl capacity

The bowl holds 8 liters. Since we have a total volume of approximately 7.153 liters, we can fit all the ingredients into the bowl.

### Step 4: Calculate remaining space in the bowl

To find out how many liters will still fit into the bowl:
\[
\text{Remaining space} = \text{Bowl capacity} - \text{Total Volume}
\]
\[
\text{Remaining space} = 8 \text{ liters} - 7.153 \text{ liters} \approx 0.847 \text{ liters}
\]

### Final Answers:

- Roger **can** use the 8-liter bowl with approximately **0.8 liters** of space remaining (rounded to the nearest tenth of a liter).

Answer 6

To determine if Roger can fit all his punch ingredients into an 8-liter bowl, we'll convert the ingredients to liters:

1. **Orange Juice (2 quarts)**:
\[
2 \times 1.06 = 2.12 \text{ liters}
\]

2. **Cranberry Juice (3 cups)**:
\[
3 \div 4.23 \approx 0.709 \text{ liters}
\]

3. **Ginger Ale (1 gallon)**:
\[
1 \div 0.26 \approx 3.85 \text{ liters}
\]

4. **Pineapple Juice (1 pint)**:
\[
1 \div 2.11 \approx 0.474 \text{ liters}
\]

### Total Volume:
\[
\text{Total} = 2.12 + 0.709 + 3.85 + 0.474 \approx 7.153 \text{ liters}
\]

### Check Against Bowl Capacity:
- **Bowl capacity**: 8 liters
- **Remaining space**:
\[
8 - 7.153 \approx 0.847 \text{ liters}
\]

**Final Answer**: Yes, Roger can use the bowl, and approximately **0.8 liters** will still fit (rounded to the nearest tenth).

Answer 7

To determine whether Roger purchased more turkey or cheese, we will convert the weight of turkey from kilograms to pounds using the conversion ratio \(1 \, \text{kilogram} \approx 2.2 \, \text{pounds}\).

1. **Turkey**:
\[
1.5 \, \text{kilograms} \times 2.2 \, \text{pounds/kilogram} = 3.3 \, \text{pounds}
\]

2. **Cheese**:
\[
2.25 \, \text{pounds}
\]

### Comparison:
- Turkey: **3.3 pounds**
- Cheese: **2.25 pounds**

**Final Answer**: Roger purchased **more turkey** (3.3 pounds vs. 2.25 pounds of cheese).

Answer 8

Roger bought:

- Turkey: **3.3 pounds**
- Beef: **2.5 pounds** (1.25 kg converted to pounds)

The chicken should weigh more than beef (2.5 pounds) but less than turkey (3.3 pounds).

**Possible weight for chicken:**
- **2.75 pounds** (rounded to the nearest hundredth).

This value satisfies the conditions given.

Answer 9

First, let's calculate the total weight of the sandwich fillings in pounds:

- **Turkey**: 1.5 kg = 3.3 pounds
- **Beef**: 1.25 kg = 2.75 pounds (1.25 kg × 2.2)
- **Cheese**: 2.25 pounds

### Total weight in pounds:
\[
\text{Total} = 3.3 + 2.75 + 2.25 = 8.3 \text{ pounds}
\]

### Convert to ounces:
\[
\text{Total in ounces} = 8.3 \text{ pounds} \times 16 \text{ ounces/pound} = 132.8 \text{ ounces}
\]

### Convert to grams:
- Convert pounds to kilograms:
\[
8.3 \text{ pounds} \div 2.2 \approx 3.77 \text{ kilograms}
\]
- Convert kilograms to grams:
\[
3.77 \text{ kg} \times 1000 \text{ grams/kg} = 3770 \text{ grams}
\]

### Comparison:
- Total weight in ounces: **132.8 ounces**
- Total weight in grams: **3770 grams**

**Final Answer**: The total weight in grams (3770 grams) is **greater** than in ounces (132.8 ounces).