Joey had 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. Her 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?
can you show me you work the problem out thank you!

Danielle
7th grade
student

Hi Danielle,

I am going to use g1 for the number of ounces that glass one holds, g2 for the number of ounces that glass 2 holds and so on. I know that

g4 = 10
g7 = 16

The last clue says that "Pouring water twice from glass 4 filled glass 8", in other words

2 g4 = g8 and thus
g8 = 20

The clue before that says "Pouring water twice from glass 3 filled glass 7" and hence

2 g3 = g7 = 16 and hence
g3 = 8

The second clue says "Pouring water from glasses 1 and 3 filled glass 5" and hence

g1 + g3 = g5 which is g1 + 8 = g5

and clue 4 is "Pouring water from glasses 1 and 5 filled glass 7" so

g1 + g5 = g7 = 16 and hence from the equation above g1 + g1 + 8 = 16

What is g1? Can you find the rest now?

Penny