For the past n days, the average (arithmetic mean) daily production…
We start with the formula for calculating the average.
average = sum/quantity
We are given that the initial quantity is n days and that the average for those n days is 50 units. We can use this to determine a sum for the n days.
Since sum = average x quantity, we know:
sum = (50) (n) = 50n
We are next given that today, the production was 90 units. This means we can add “1” to the current quantity and “90” to the current sum. We are also given that this new average is 55 units per day. Substituting this information into the average formula we get:
55 = (50n + 90)/(n + 1)
55(n + 1) = 50n + 90
55n + 55 = 50n + 90
5n = 35
n = 7 days