SOLUTION: Beatrice's brewpub analyzed their sales data for the last year and found that the number of beers bb sold in a day varies directly with the square of the temperature tt and inverse

Question 1093504: Beatrice's brewpub analyzed their sales data for the last year and found that the number of beers bb sold in a day varies directly with the square of the temperature tt and inversely with the number of events happening on campus cc. Over the summer, when c=4c=4 and t=82t=82, they sold b=1681b=1681 beers in one day! How many beers should Beatrice expect to sell on a day with 6 events and a temperature of 70 degrees? Round your answer to the nearest whole number.
Answer by greenestamps(13219) (Show Source): You can put this solution on YOUR website!

This is a very strangely worded problem. Did you get it like this from a book, or online, or something like that, or is this your own wording of the problem? The use of double letters for the variables is very unusual; and I don't see the significance (or meaning) of a statement like "c=4c=4". Finally, the whole concept is not scientifically valid, since it assumes a temperature of 0 degrees (Fahrenheit, I assume!) has some special physical meaning.

Nevertheless, when we get past the very poor presentation of the problem, there is some useful mathematics to be found.

We have the number of beers sold, b, being directly proportional to the square of the temperature (in Fahrenheit), t, and inversely proportional to the number of events on campus, c. The equation of proportionality is then

where k is a constant to be determined. Plugging the given numbers (b=1681, t=82, c=4) into the equation, we see that this is a contrived problem, as the constant k turns out to have the value exactly 1. So now the formula for the number of beers sold is

Plugging in the new values of t and c, we find the number of beers sold, to the nearest whole number, is

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