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
First, let's convert all the ingredients to liters using the conversions provided.
2 quarts orange juice:
2 quarts x 1.06 liters/quart = 2.12 liters
3 cups cranberry juice:
3 cups x (1 liter / 4.23 cups) = 3 / 4.23 liters ≈ 0.71 liters
1 gallon ginger ale:
1 gallon x 0.26 liters/gallon = 0.26 liters
1 pint pineapple juice:
1 pint x 2.11 liters/pint = 2.11 liters
Now, let's sum up the liters of all ingredients to see if they fit into the 8-liter bowl:
Total liters = Orange juice + Cranberry juice + Ginger ale + Pineapple juice
Total liters = 2.12 liters + 0.71 liters + 0.26 liters + 2.11 liters
Total liters ≈ 2.12 + 0.71 + 0.26 + 2.11
Total liters ≈ 5.20 liters
Roger's bowl holds 8 liters, so let's determine if all the punch ingredients will fit:
8 liters - 5.20 liters = 2.8 liters of free space available.
Since 5.20 liters is less than 8 liters, Roger can use the bowl to mix all the ingredients for the punch. To determine how much more liquid he could still fit into the bowl, we round 2.8 liters to the nearest tenth:
Free space available in the bowl ≈ 2.8 liters (rounded to the nearest tenth, it remains 2.8 liters).
So, Roger can definitely use the 8-liter bowl for his punch, and he will have an additional 2.8 liters of space left in the bowl for more punch or other additions if he desires.