At the end of year 1998, Shepherd bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > 0. If Shepherd had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true? radio_button_unchecked p = q radio_button_unchecked p < q radio_button_unchecked p > q radio_button_unchecked p = q/2
Question
At the end of year 1998, Shepherd bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > 0. If Shepherd had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?
radio_button_unchecked p = q
radio_button_unchecked p < q
radio_button_unchecked p > q
radio_button_unchecked p = q/2
Solution
To solve this problem, we need to understand that the number of goats at the end of 1998 is the same as the number of goats at the end of 2002. This means that the rate of increase (p%) and the rate of decrease (q%) must be equal to keep the number of goats constant over this period. Therefore, the correct answer is:
radio_button_checked p = q
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