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Question 229031: How can you use unmarked 7 quart and 4 quart containers to measure out exactly one quart? two quarts? three quarts? five quarts
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll walk you through the first two subproblems
Making one quart:
Step 1) Completely fill the 4 quart container
Step 2) Drain all of the water from the 4 quart container into the 7 quart container. There are 4 quarts of water in the 7 quart container. This means that there are 3 quarts of empty space left over.
Step 3) Repeat steps 1 and 2, but make sure not to spill or overflow. After this is done, the 7 quart container is full. Because the remaining 3 qts are occupied, and there are 4 qts in the other container, this tells us that 1 quart of water is left in the 4 qt container, which is exactly what we want.
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Making Two Quarts
Step 1) Fill the 7 qt container (completely)
Step 2) Use the water in the 7 qt container to completely fill the 4 qt container. There are now 3 qts left in the 7 qt container.
Step 3) Completely empty the 4 qt container.
Step 4) Dump the 3 qts of water that's in the 7 qt container into the 4 qt container. So the 7 qt container is completely empty now while there are 3 qts in the 4 qt container (so there's room for one more qt).
Step 5) Completely fill the 7 qt container.
Step 6) Use the water in the 7 qt container to completely fill up the 4 qt container. Since there was room for one more quart, this means that there are 7-1=6 qts left over in the 7 qt container.
Step 7) Dump all of the water out of the 4 qt container.
Step 8) Use the water in the 7 qt container to fill up the 4 qt container. Since we're taking 4 qts away from 6, we end up with 6-4=2 qts leftover in the 7 qt container (which is what we want).
I'll let you tackle the other two.
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