Question 1

Question

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

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.

1. Orange juice (2 quarts):

   • Conversion: 1 quart ≈ 0.946 liters $$2\text{ quarts}\times 0.946\text{ liters/quart}=1.892\text{ liters}$$

2. Cranberry juice (3 cups):

   • Conversion: 1 liter ≈ 4.23 cups $$3\text{ cups}\times \frac{1\text{ liter}}{4.23\text{ cups}}\approx 0.709\text{ liters}$$

3. Ginger ale (1 gallon):

   • Conversion: 1 gallon ≈ 3.785 liters $$1\text{ gallon}\approx 3.785\text{ liters}$$

4. Pineapple juice (1 pint):

   • Conversion: 1 pint ≈ 0.473 liters $$1\text{ pint}\approx 0.473\text{ liters}$$

Step 2: Add up all the converted amounts. $$\text{Total volume}=(1.892\text{ liters})+(0.709\text{ liters})+(3.785\text{ liters})+(0.473\text{ liters})$$

Calculating the total: $$1.892+0.709+3.785+0.473=7.859\text{ liters}$$

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

Since $7.859\text{ liters}<8\text{ liters}$, Roger can use the bowl.

Step 4: Calculate how much space will be left in the bowl. $$\text{Extra space}=8\text{ liters}-7.859\text{ liters}=0.141\text{ liters}$$

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

Answer 2

for my final calculation of how many liters the ingredients lead up to i got 17.18 liters

Answer 3

Let's re-evaluate the conversion for each ingredient step-by-step to ensure accuracy.

Here are the ingredients and their conversions again:

1. Orange juice: 2 quarts

   • Conversion: 1 quart ≈ 0.946 liters
     $$2\text{ quarts}\times 0.946\text{ liters/quart}=1.892\text{ liters}$$

2. Cranberry juice: 3 cups

   • Conversion: 1 liter ≈ 4.23 cups
     $$3\text{ cups}\times \frac{1\text{ liter}}{4.23\text{ cups}}\approx 0.709\text{ liters}$$

3. Ginger ale: 1 gallon

   • Conversion: 1 gallon ≈ 3.785 liters
     $$1\text{ gallon}\approx 3.785\text{ liters}$$

4. Pineapple juice: 1 pint

   • Conversion: 1 pint ≈ 0.473 liters
     $$1\text{ pint}\approx 0.473\text{ liters}$$

Now, let's add them up again:

$$\text{Total volume}=1.892\text{ liters (orange juice)}+0.709\text{ liters (cranberry juice)}+3.785\text{ liters (ginger ale)}+0.473\text{ liters (pineapple juice)}$$

Calculating: $$1.892+0.709+3.785+0.473=7.859\text{ liters}$$

With this re-evaluation, the total indeed comes up to 7.859 liters.

If you arrived at 17.18 liters, it might suggest a mistake in conversions or in adding up the quantities. Please check each ingredient's conversion again or let me know how you calculated that total, and we can figure it out together!