If the average (arithmetic mean) of x, y, and 40 is 5 greater than the average of x, y, 40, and 60, find the average of x and y.
Answers
A) 100 B) 110 C) 120 D) 140 E) 150
consider the statement "9 is 5 greater than 4": 9 = 4 + 5   similarly,   the average of x, y, and 40 = (the average of x, y, 40, and 60) + 5   (x+y+40)/3 = (x+y+40+60)/4 + 5   (x+y+40)/3 = (x+y+100)/4 + 5   get a common denominator on the right side   (x+y+40)/3 = (x+y+100)/4 + 20/4   (x+y+40)/3 = (x+y+100+20)/4   (x+y+40)/3 = (x+y+120)/4   cross multiply   4(x+y+40) = 3(x+y+120)   4x+4x+160 = 3x+3y+360   collect like terms   4x-3x+4y-3y = 360 - 160   x + y = 200   thus   (x+y)/2 = 200/2   (x+y)/2 = 100   the average of x and y is 100   100
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If the average (arithmetic mean) of x, y, and 40 is 5 greater than the average of x, y, 40, and 60, find the average of x and y.