Two Weeks in the Village: The Olympics Continue - The Solutions

 

September 25, 2000


The percent increase is simply the difference in price, divided by the price in 1896, times 100, which is [(39.72 - 0.16) \ 0.16] x 100 = 24,725%. That's just the mathematical way of saying that the price has increased a lot.

 

Let's say the price per ticket increased x percent from one Olympic games to the next. So, if the price was 16 cents at the first Olympics,

    * the price at the second Olympics was 0.16 (1 + x/100);
    * the price at the third Olympics was 0.16 (1 + x/100) (1 + x/100), or 0.16 (1 + x/100)2;
    * the price at the fourth Olympics was 0.16 (1 + x/100)3,
    * and so on.

 

Since the Summer Games 2000 represent the XXVII Olympiad (the 27th Olympics), the price at this year's event must be 0.16 (1 +x/100)26, and we know that equals 37.92. A little trial and error with a calculator will approximately show that x = 23, which means that ticket prices increased, on average, 23% per year. From 1896 to 1920, prices must have increased five times, so the price of a ticket at the 1920 Olympics could be estimated as 0.16 (1 + 23/100)6 = 0.55, or about 55 cents.

 

One kilometer is approximately 0.62 miles, or 5280 x 0.62 = 3274 feet. So, the Olympic Village will need 15,000 x 3274 = 49,110,000 feet of toilet paper, which is equal to 49,110,000 x 12 = 589,320,000 inches. Now, one square of toilet paper is 4 inches, and a roll usually contains 100 squares, so a roll has 4 x 100 = 400 inches of toilet paper. Hence, a total of 589,320,000 / 400 = 1,473,300 rolls will be needed. (Buy stock in Charmin!)

 

Since 50 meters is one-half of 100, it would take de Bruijn 24.13 + 24.13 = 48.26 seconds (assuming she could hold the same pace). Jones would be waiting 48.26 - 10.83 = 37.43 seconds.

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