Find the average of x and y if the average (arithmetic mean) of x, y, and 30 is 10 greater than the average of x, y, 20, and 30.
Choose the correct choice from the following choices:  A) 50  B) 75  C) 100  D) 125  E) 150
consider 30 is 10 greater than 20: 30 = 20+10   similarly   (x+y+30)/3 = (x+y+20+30)/4 + 10   get a like denominator on the right side   (x+y+30)/3 = (x+y+50)/4 + 40/4   (x+y+30)/3 = (x+y+50+40)/4   (x+y+30)/3 = (x+y+90)/4   cross multiply   4(x+y+30) = 3(x+y+90)   4x+4y+120 = 3x+3y+270   collect like terms   4x-3x + 4y-3y = 270 - 120   x + y = 150   thus (x+y)/2 = 150/2   (x+y)/2 = 75   the average of x and y is 75   75
<result>B</result>
Find the average of x and y if the average (arithmetic mean) of x, y, and 30 is 10 greater than the average of x, y, 20, and 30.