The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. The average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time?
To find the average number of shoppers in the new store at any time, we need to calculate the number of shoppers who enter the store per hour and multiply it by the average time each shopper spends in the store.
The number of shoppers who enter the new store per hour is 90.
Each shopper stays for an average of 12 minutes, which is equivalent to 12/60 = 1/5 of an hour.
So, the average number of shoppers in the new store at any time is 90 * 1/5 = <<90*1/5=18>>18.
Let's assume that the average number of shoppers in the original store at any time is x.
To calculate the percentage difference between the average number of shoppers in the new store and the original store, we can use the formula: (x - 18) / x * 100.
Simplifying this expression gives us: (x - 18) / x * 100 = (x * 100 - 1800) / x.
Therefore, the average number of shoppers in the new store at any time is (x * 100 - 1800) / x percent less than the average number of shoppers in the original store at any time.
To find the average number of shoppers in the new store at any time, we need to calculate the number of shoppers entering the store per minute and the number of shoppers leaving the store per minute.
First, let's find the number of shoppers entering per minute. Since the average number of shoppers entering per hour is 90, we divide this by 60 to get the number of shoppers entering per minute: 90 shoppers/hour ÷ 60 minutes/hour = 1.5 shoppers/minute.
Next, let's find the number of shoppers leaving per minute. Since each shopper stays for an average of 12 minutes, we can calculate the average number of shoppers leaving per minute by dividing the average number of shoppers per minute by the average time each shopper stays: 1.5 shoppers/minute ÷ 12 minutes/shopper = 0.125 shoppers/minute.
Now, let's find the average number of shoppers in the new store at any time. This can be calculated by subtracting the number of shoppers leaving per minute from the number of shoppers entering per minute: 1.5 shoppers/minute - 0.125 shoppers/minute = 1.375 shoppers/minute.
To find the percentage by which the average number of shoppers in the new store is less than the average number of shoppers in the original store, we need to find the difference in the average number of shoppers. Let's assume the average number of shoppers in the original store at any time is 100 shoppers.
The difference is then calculated by subtracting the average number of shoppers in the new store (1.375 shoppers/minute) from the average number of shoppers in the original store (100 shoppers): 100 shoppers - 1.375 shoppers/minute = 98.625 shoppers.
To find the percentage difference, we divide the difference (98.625 shoppers) by the average number of shoppers in the original store (100 shoppers) and multiply by 100: (98.625 shoppers / 100 shoppers) × 100 = 98.625%.
Therefore, the average number of shoppers in the new store at any time is approximately 98.625% less than the average number of shoppers in the original store at any time.