### Brain Teasers

# Filling Glasses

Joey has 8 drinking glasses, all of different sizes. He has lined them up from smallest to largest and numbered them #1 (smallest) to #8 (largest). He knows that glass #4 holds 10 ounces and that glass #7 holds a pint, or 16 ounces. Now he wants to figure out how much all the others hold!

He experiments by filling up different glasses with water and pouring the water back and forth into other glasses. Here are his results:

Pouring water from glasses #1 and #2 filled glass #4.

Pouring water from glasses #1 and #3 filled glass #5.

Pouring water from glasses #2 and #3 filled glass #6.

Pouring water from glasses #1 and #5 filled glass #7.

Pouring water from glasses #1 and #7 filled glass #8.

Pouring water twice from glass #3 filled glass #7.

Pouring water twice from glass #4 filled glass #8.

How much water does each glass hold?

He experiments by filling up different glasses with water and pouring the water back and forth into other glasses. Here are his results:

Pouring water from glasses #1 and #2 filled glass #4.

Pouring water from glasses #1 and #3 filled glass #5.

Pouring water from glasses #2 and #3 filled glass #6.

Pouring water from glasses #1 and #5 filled glass #7.

Pouring water from glasses #1 and #7 filled glass #8.

Pouring water twice from glass #3 filled glass #7.

Pouring water twice from glass #4 filled glass #8.

How much water does each glass hold?

### Hint

Rewrite each experiment as an equation, and then substitute the known quantities for #4 and #7 into the equations wherever you can.### Answer

#1 holds 4 ounces#2 holds 6 ounces

#3 holds 8 ounces

#4 holds 10 ounces

#5 holds 12 ounces

#6 holds 14 ounces

#7 holds 16 ounces

#8 holds 20 ounces

To begin with, you know that glass #4 holds 10 ounces and that glass #7 holds 16 ounces. With this information and the given clues, you can quickly determine that glass #8 holds 20 ounces (10 ounces x 2 = 20 ounces) and that glass #3 holds 8 ounces (16 ounces / 2 = 8 ounces).

Now you can substitute for the remaining equations and find that:

Since #7 holds 16 ounces and #7 + #1 = #8, then #1 must hold 4 ounces (20 - 16 = 4).

Since #1 + #2 = #4, then #2 must hold 6 ounces (10 - 4 = 6).

Since #1 + #5 = #7, then #5 must hold 12 ounces (16 - 4 = 12).

Since #2 + #3 = #6, then #6 must hold 14 ounces (6 + 8 = 14).

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