Find the average (arithmetic mean) of x and y if the average of x, y, and 5 is 20 more than the average of x, y, 5, and 15.  Pick one:
A) 110	B) 120	C) 130	D) 140	E) 150
consider the statement 50 is 20 more than 30: 50 = 30+20   similarly   the average of x, y, and 5 = (the average of x, y, 5, and 15) + 20   (x+y+5)/3 = (x+y+5+15)/4 + 20   (x+y+5)/3 = (x+y+20)/4 + 20   (x+y+5)/3 = (x+y+20)/4 + 80/4   (x+y+5)/3 = (x+y+20+80)/4   (x+y+5)/3 = (x+y+100)/4   cross multiply   4(x+y+5) = 3(x+y+100)   4x+4y+20 = 3x+3y+300   4x-3x +4y-3y = 300 - 20   x + y = 280   so   (x+y)/2 = 280/2   (x+y)/2 = 140   i.e the average of x and y is 140   140
<result>D</result>
Find the average (arithmetic mean) of x and y if the average of x, y, and 5 is 20 more than the average of x, y, 5, and 15.