Problem of the Week 5

On the plant ZOG, colored coins are used for money.  Suppose 12 white, 9 red, 8 yellow, 4 blue, and 0 green coins can be exchanged for 2 white, 1 red, 0 yellow, 1 blue, and 1 green coin.  Also, suppose 1 green = n blue, 1 blue = n yellow, 1 yellow = n red, and 1 red = n white.

What is the whole number rate of exchange for these coins?

Is there only one exchange rate possible or are there multiple exchange rates possible?


Alternate Problem 5

Alice, Bob, Carla, and Denny each have a different kind of measuring stick.  Each stick is marked with equally spaced units, but the spaces are not necessarily the same from one stick to another.  Alice’s, Bob’s, and Denny’s sticks each have been broken off at the beginning of their scales.  Carla’s is not broken.  Alice’s scale starts at 11, Bob’s at 33, Carla’s at 0, and Denny’s at 17.

Each of the four people measured the depth of a pond at the same spot.  Alice’s stick read 91; Bob’s stick read 113; Carla’s read 160; and Denny’s read 177.  Then, with his stick, Denny measured Carla’s height.  His stick read 89.  What reading would Alice’s measuring stick give for Carla’s height?


Extension Problem 5

Scientist Cindy Grade has developed a new thermometer.  Unlike the thermometer developed by Gabriel Fahrenheit, where 32°F marks the freezing point of water and 212°F marks the boiling point, Dr. Grade’s thermometer reads 0°G for the freezing point and 150°G for the boiling point, respectively.  All readings are taken at sea level.

Write a formula that expresses the relationship between the Grade scale (G) and the Fahrenheit scale (F).

Do the two scales ever agree?  If so, at what temperature reading?