Question

A Penteria is a special (fictional) kind of bacteria such that, regardless of the original population in a collection, the population increases by $5$ every minute. Additionally, at the end of every hour, all but the initial ones die. If $137$ Penteria are alive after $506$ minutes, how many were there at the beginning?

Answer 1

To determine the initial number of Penteria bacteria, we subtract the population growth within the last partial hour from the total number after 506 minutes. Since the population increases by 5 every minute and resets every hour, we calculate growth for the 26 minutes of the last incomplete hour. There were initially 7 Penteria at the beginning.

Step-by-step explanation:

To solve the problem regarding the Penteria population, we need to consider the characteristics of the population dynamics. The key information is that the population of Penteria increases by 5 every minute but resets to the original number at the end of every hour. Given that there are 137 Penteria after 506 minutes, we must first determine how many complete hours have passed, because after each hour, the population reset to its initial number.

We divide 506 by 60, which is the number of minutes in an hour, to get 8 hours and 26 minutes. Since at the end of 8 hours, the count would have reset to the initial number, we only need to consider the population increase over the last 26 minutes. Since the population increases by 5 every minute, we multiply the 26 minutes by 5 to find the population growth during that period, which is 130. So, after 506 minutes, the population increased by 130 from its original number to make 137 (since 137 - 130 = 7), meaning there were originally 7 Penteria at the beginning.