Restaurant Review and Inverse Proportions

The following quote was copied from the "Neighborhood Dish" column found in the "Dining Section" of the Tempe Republic on 6 April 2007.

   "There seems to be a mathematical equation in dining:
    There is an inverse proportional relationship between
    the number of TV screens in a sports bar and the quality
    of the food."

[wikipedia] "Two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio."

   y = k ⋅ x, where 'k' is a constant

[wikipedia] "Two variables are inversely proportional (or varying inversely) if one of the variables is directly proportional with the multiplicative inverse of the other, or equivalently if their product is a constant."

   k = x ⋅ y

[wikipedia] "The multiplicative inverse of a number x, denoted 1/x or x-1, is the number which, when multiplied by x, yields 1. The multiplicative inverse of x is also called the reciprocal of x."

Exercises
  1. Briefly explain what is meant by "mathematical equation."

  2. No or Yes: Zero does not have a reciprocal.

  3. No or Yes: n ⋅ n-1 = 1 for all values of 'n'.

  4. No or Yes: The multiplicative inverse of 0.25 is 4.

  5. The circumference 'C' of a circle is directly proportional to its diameter 'd'.

       C = Pi ⋅ d
    

    The constant of proportionality is _________.

  6. The "mass-energy equivalence" formula states that "when a body has a mass, it has a certain energy equivalence, even 'at rest'."

    	E = m ⋅ c^2
    
    	where
    
    	E = energy equivalent to the mass (in joules)
    	m = mass (in kilograms)
    	c = speed of light in a vacuum (299,792,458 meters per second)
    	    [c comes from the Latin word Celeritas (swiftness)]
    

    In the mass-energy equivalence formula, the constant of proportionality is __________________ miles per hour squared. [kilo- is 10^3; 1 kilometer = 0.621371192 mile]

  7. Let's pretend that the food quality of a restaurant is scored on a scale of 100 to 0, with 100 being "beyond excellent" and anything less than one as "deadly." Every restaurant is assigned a food rating 'r' prior to opening that remains constant for the entire life of the restaurant. If a restaurant has zero or one TVs, its food quality 'q' equals its food rating 'r'; otherwise, its food quality 'q' is indirectly proportional its food rating 'r' divided-by the number of TVs.

       if t = 0 or t = 1, then 
          q = r
       else 
          q = r / t
    

    Foogoo BBQ located in Timbuktu opened with an food rating of 94. After two months of operation, Foogoo BBQ installed its first TV and its food quality score fell to __________. Foogoo BBQ installed two additional TVs over the next three months causing its food quality score to become _________. Foogoo BBQ's food quality will turn "deadly" if it installs TV number _______.


Creator: Gerald D. Thurman [gthurman@gmail.com]
Created: 08 April 2007

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This work is licensed under a Creative Commons License.