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Pouring

Created by Inna Shapiro ©2007

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Problem 1Marty has two cans: a small one (5 qt) and a large one (7 qt).How can he get 6 qt of water from a tap?

We are using the base volume units1 gallon /gal/ =4 quarts /qt/1 quart /qt/ = 2 pints /pt/

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AnswerMarty can follow the next steps:1. Fill the large can with 7 qt of water.2. Pour 5 qt of water from the large can to the small

can.3. Empty the small can.4. Pour the remaining 2 qt of water from the large can

to the small can.5. Fill the large can from a tap.6. Fill the small can from the large can.7. Empty the small can.8. Pour the remaining 4 qt of water from the large can

to the small can.9. Fill the large can from a tap.10. Fill the small can from the large can. Now Marty

has 6 qt of water in the large can.

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Answer /continued/

Step 1 2 3 4 5 6 7 8 9 10

Large

can

7 2 2 0 7 4 4 0 7 6

Small

can

0 5 0 2 2 5 0 4 4 5

These 10 steps are summarized in the following table:

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Problem 2

There are two buckets – 4 qt and 9 qt.How can you get 6 qt of water from a river?

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AnswerYou can follow these steps:

Step 1 2 3 4 5 6 7 8

Large

can

9 5 5 1 1 0 9 6

Small

can

0 4 0 4 0 1 1 4

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Problem 3

Kathy has two cans – 3 qt and 5 qt.How can she pour 4 qt of water from a tap?

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AnswerKathy can use the following table:

Step 1 2 3 4 5 6

Large

can

5 2 2 0 5 4

Small

can

0 3 0 2 2 3

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Problem 4

There are three buckets: 10qt, 7qt, and 3qt. The large bucket is full of milk.How can you pour 5 qt of milk into the medium bucket?

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AnswerYou can follow these steps:

Step 1 2 3 4 5 6 7 8 9

Large bucket

10 3 3 6 6 9 9 2 2

Medium bucket

0 7 4 4 1 1 0 7 5

Small bucket

0 0 3 0 3 0 1 1 3

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Problem 5

There are more than 13 gal of gasoline in a container. A driver has two cans – a 9 gal can and a 5 gal can.How can he get 8 gal of gasoline?

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AnswerThe driver can use the following table:

Step 1 2 3 4 5 6 7

Container >13 >4 >4 >9 >9 >0 >0

Large can

0 9 4 4 0 9 8

Small can 0 0 5 0 4 4 5

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Problem 6

A large can /12 gal/ is full of milk.A farmer has two empty cans – a small one /5 gal/ and a medium one /8 gal/.How can the farmer divide the milk equally between two cans?

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Answer

Step 1 2 3 4 5 6 7 8

Large can

12 4 4 9 9 1 1 6

Medium can

0 8 3 3 0 8 6 6

Small can 0 0 5 0 3 3 5 0

The farmer can follow these steps:

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Problem 7

Bill knows that there are more than 10 pt of water in a a can. He has two pots – a small one /5pt/ and a large one /9 pt/.How can he get exactly 6 pt of water?

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AnswerBill can use the following table:

Step 1 2 3 4 5 6 7 8 9 10 11 12 13

Can >10 >1 >1 >6 >6 >5 >5 >0 >0 >9 >9 >4 >4

Large pot

0 9 4 4 0 0 5 5 9 0 1 1 6

Small pot

0 0 5 0 4 5 0 5 1 1 0 5 0

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Problem 8

There are 18 qt of water in a bucket and three empty pots – 7 qt, 7 qt, and 4 qt. How can you put 6 qt of water in the bucket and 6 qt in each of the two bigger pots?

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AnswerYou can follow the next steps:

Step 1 2 3 4 5 6 7 8 9 10

Bucket 18 11 11 11 7 7 8 8 8 12

1-st pot

7 qt

0 7 3 3 3 3 3 3 6 6

2-d pot

7 qt

0 0 0 4 4 7 7 3 0 0

3-d pot

4 qt

0 0 4 0 4 1 0 4 4 0

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Answer /continued/

Step 11 12 13 14 15 16 17

Bucket 5 5 9 9 2 2 6

1-st pot

7 qt

6 6 6 6 6 6 6

2-d pot

7 qt

7 3 3 0 7 6 6

3-d pot

4 qt

0 4 0 3 3 4 0

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Problem 9

Peter has three cans: 6 qt, 7 qt, and 3 qt. He knows that there is 4 qt of water in the first can and 6 qt of water in the second one.

How can he pour half of the water into one can?

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Answer

Step 1 2 3 4 5 6

1-st can

6 qt

4 1 1 6 5 5

2-d can

7 qt

6 6 7 2 2 5

3-d can

3 qt

0 3 2 2 3 0

Peter can use the following table:

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Problem 10Grandma put two equal cups – a cup of coffee and a cup of milk - on a table. Then she poured one tablespoon of milk in the cup of coffee and stirred it. After that she poured one tablespoon from the cup of coffee in the cup of milk.Which is now bigger – the volume of coffee in the cup of milk or the volume of milk in the cup of coffee?

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AnswerLet’s look at the cup that originally had only coffee. Suppose the volume of that cup is V, and the volume of milk in it is M. The remaining volume in this cup is V-M, and it is coffee. The rest of the coffee that was originally in that cup is now in the other cup. So the amount of coffee in the milk isV- (V- M) = MThat means Grandma gets the same amounts of coffee in the milk and milk in the coffee.