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
To answer Roger's question, first we'll need to convert all of the ingredients into liters using the provided measurement equivalents. After that, we can check if the total volume is less or greater than 8 liters.
Here's the conversion for each ingredient:
1. **Orange Juice**: 2 quarts
Since 1 quart is approximately 1.06 liters, 2 quarts will be:
2 * 1.06 = 2.12 liters
2. **Cranberry Juice**: 3 cups
As 1 liter is about 4.23 cups, we will divide the number of cups by 4.23 to find out how many liters it is:
3 / 4.23 ≈ 0.7097 liters
3. **Ginger Ale**: 1 gallon
Knowing that 1 gallon is approximately 0.26 liters, 1 gallon will be:
1 / 0.26 ≈ 3.8462 liters
4. **Pineapple Juice**: 1 pint
Since 1 pint is about 2.11 pints per liter, 1 pint will be:
1 / 2.11 ≈ 0.4739 liters
Next, we'll sum up all these converted values to check the total volume:
Total volume = 2.12 (Orange Juice) + 0.710 (Cranberry Juice) + 3.846 (Ginger Ale) + 0.474 (Pineapple Juice)
Calculating out the sum:
Total volume ≈ 2.12 + 0.710 + 3.846 + 0.474
Total volume ≈ 7.150 liters
Now let's compare the total volume against the bowl's capacity, which is 8 liters:
8 liters (bowl capacity) - 7.150 liters (total punch ingredients) = 0.850 liters
Since the total volume of ingredients is less than the 8 liters capacity of the bowl, Roger can use the bowl to mix all the ingredients for the punch.
Rounding to the nearest tenth:
0.850 liters ≈ 0.9 liters
Roger has approximately 0.9 liters of free space left in the bowl after mixing all the ingredients.