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 deeds 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 determine if Roger can use the 8-liter bowl to mix all the ingredients for the punch, we need to convert the quantities of each ingredient to liters.
2 quarts orange juice = 2 * 1.06 = 2.12 liters
3 cups cranberry juice = 3 * 4.23 / 4 = 3.1775 liters (rounded to the nearest tenth)
1 gallon ginger ale = 1 * 3.785 = 3.785 liters
1 pint pineapple juice = 1 * 2.11 / 4 = 0.5275 liters (rounded to the nearest tenth)
Total volume of all ingredients = 2.12 + 3.1775 + 3.785 + 0.5275 = 9.609 liters (rounded to the nearest thousandth)
Since the total volume of all the ingredients is 9.609 liters, which is greater than the capacity of the 8-liter bowl, Roger cannot use the bowl to mix all the ingredients at once.
To determine how many extra liters of liquid there are, we subtract the capacity of the bowl (8 liters) from the total volume of all the ingredients (9.609 liters).
Extra liters of liquid = 9.609 - 8 = 1.609 liters (rounded to the nearest thousandth)
Therefore, there are approximately 1.6 extra liters of liquid that cannot fit in the 8-liter bowl.