Find the average (arithmetic mean) of x and y if the average of x, y, and 50 is 20 more than the average of x, y, 50, and 70.  Select the correct option
A) 100 B) 120 C) 140 D) 180 E) 200
consider "60 is 20 more than 40": 60 = 40 + 20   similarly   (x+y+50)/3 = (x+y+50+70)/4 + 20   (x+y+50)/3 = (x+y+120)/4 + 80/4   (x+y+50)/3 = (x+y+120+80)/4   (x+y+50)/3 = (x+y+200)/4   cross multiply   4(x+y+50) = 3(x+y+200)   4x+4y+200 = 3x+3y+600   4x-3x +4y-3y = 600 - 200   x + y = 400   so   (x+y)/2 = 400/2   (x+y)/2 = 200   thus the average of x and y is 200   200
<result>E</result>
Find the average (arithmetic mean) of x and y if the average of x, y, and 50 is 20 more than the average of x, y, 50, and 70.