At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 80 customers per day, what is the value of x?  Choose the correct answer:
A) 2 B) 5 C) 7 D) 8 E) 20

Rationale: "withoutusing the formula , we can see that today the restaurant served 40 customers above the average . the total amount above the average must equal total amount below the average . this additional 40 customers must offset the “ deficit ” below the average of 80 created on the x days the restaurant served only 75 customers per day . 40 / 5 = 8 days . choice ( a ) . withthe formula , we can set up the following : 80 = ( 75 x + 120 ) / ( x + 1 ) 80 x + 80 = 75 x + 120 5 x = 40 x = 8 answer choice ( d )"
Answer: D