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Party Punch

Solution

They began with 6 gallons of punch in the bowls.

Explanation

Here is a summary of the story. Read the details below to work backward and solve the problem.

Problem: How many gallons were in the bowls at the start?

• less the 34 cups they served during the first intermission
• plus the amount the sixth-graders added, made after the first intermission (during the second act)
• less the quantity served during the second intermission

The result is the 2 gallons of punch at the end of the performance.

To find out how many gallons they had to begin with, work backward, starting with the 2 gallons left at the end of the performance. When working backward, reverse the operations that occurred in the story from beginning to end. Do this by following the steps below.

One way to solve the problem is to change all the quantities to ounces.

1 cup = 8 oz
1 pint = 2 cups = 2 x 8 oz = 16 ounces
1 quart = 2 pints = 2 x 16 oz = 32 ounces
1 gallon = 4 quarts = 4 x 32 oz = 128 ounces

Step	Amount	Calculation	Result
Begin with what was left at the end.	2 gallons of punch	2 x 128 oz = 256 oz	256 oz
Calculate the amount served during the second intermission.	7 quarts 18 cups 25 half-cup glasses	7 x 32 oz = 224 oz 18 x 8 oz = 144 oz 25 x 4 oz = 100 oz total: 468 oz	468 oz
Add, to find out how much they had before the second intermission.		256 oz + 468 oz 724 oz	724 oz
Calculate the amount made between the two intermissions.	2 quarts of orange juice 2 quarts of ginger ale 2 12-ounce cans of fruit juice concentrate 6 12-ounce cans of water 4 ounces of pineapple juice	2 x 32 oz = 64 oz 2 x 32 oz = 64 oz 2 x 12 oz = 24 oz 6 x 12 oz = 72 oz 1 x 4 oz = 4 oz total: 228 oz	228 oz
Subtract, to find out how much they had after the first intermission.		724 oz − 228 oz 496 oz	496 oz
Calculate the amount served during the first intermission.	34 cups of punch	34 x 8 oz = 272 oz	272 oz
Add, to find out how many ounces of punch they had before the first intermission.		496 oz + 272 oz 768 oz	768 oz
Divide, to find out the equivalent number in gallons	There are 128 ounces in a gallon.	768 oz ÷ 128 oz =	6 gal

This problem can also be solved by converting the liquid to another unit, but be careful about the conversions and computing correctly with fractions.

For those who have solved the problem using cups, here is a summary of the results in cups after each step:

Step	Amount	Calculation	Result
Begin with what was left at the end.	2 gallons of punch	2 x 128 oz = 256 oz	256 oz = 32 cups
Calculate the amount served during the second intermission.	7 quarts 18 cups 25 half-cup glasses	7 x 32 oz = 224 oz 18 x 8 oz = 144 oz 25 x 4 oz = 100 oz total: 468 oz	468 oz = 58.5 cups
Add, to find out how much they had before the second intermission.		256 oz + 468 oz 724 oz	724 oz = 90.5 cups
Calculate the amount made between the two intermissions.	2 quarts of orange juice 2 quarts of ginger ale 2 12-ounce cans of fruit juice concentrate 6 12-ounce cans of water 4 ounces of pineapple juice	2 x 32 oz = 64 oz 2 x 32 oz = 64 oz 2 x 12 oz = 24 oz 6 x 12 oz = 72 oz 1 x 4 oz = 4 oz total: 228 oz	228 oz = 28.5 cups
Subtract, to find out how much they had after the first intermission.		724 oz − 228 oz 496oz	496 oz = 62 cups
Calculate the amount served during the first intermission.	34 cups of punch	34 x 8 oz = 272 oz	272 oz = 34 cups
Add, to find out how many ounces of punch they had before the first intermission.		496 oz + 272 oz 768 oz	768 oz = 96 cups
Divide, to find out the equivalent number in gallons.	There are 128 ounces in a gallon.	768 oz ÷ 128 oz = OR 96 cups divided by 16 cups to a gallon	6 gal