Find the average (arithmetic mean) of x and y if the average of x, y, and 10 is 20 greater than the average of x, y, 10, and 20.  Choose the correct choice from the following answers
A) 115
B) 130
C) 145
D) 160
E) 175
consider the statement 30 is 20 greater than 10: 30 = 10 + 20   similarly   the average of x, y, and 10 = (the average of x, y, 10, and 20) + 20   (x+y+10)/3 = (x+y+10+20)/4 + 20   (x+y+10)/3 = (x+y+30)/4 + 80/4   (x+y+10)/3 = (x+y+30+80)/4   (x+y+10)/3 = (x+y+110)/4   cross multiply   4(x+y+10) = 3(x+y+110)   4x+4y+40 = 3x+3y+330   4x-3x + 4y-3y = 330 - 40   x + y = 290   thus   (x+y)/2 = 290/2   (x+y)/2 = 145   thus the average of x and y is 145   145
<result>C</result>
Find the average (arithmetic mean) of x and y if the average of x, y, and 10 is 20 greater than the average of x, y, 10, and 20.